Updated on 2021/11/05

写真a

 
Sho Matsumoto
 
Organization
Research Field in Science, Science and Engineering Area Graduate School of Science and Engineering (Science) Department of Science Mathematics and Informatics Program Associate Professor
Title
Associate Professor
Profile
表現論、ランダム行列とその周辺の研究

Degree

  • 博士(数理学) ( 2007.3   九州大学 )

Research Interests

  • symmetric group

  • random matrix

  • symmetric function

Research Areas

  • Natural Science / Basic analysis  / Probability Theory

  • Natural Science / Algebra  / Representation Theory, Algebraic Combinatorics

Research History

  • Kagoshima University   Research Field in Science, Science and Engineering Area Graduate School of Science and Engineering (Science) Department of Science Mathematics and Informatics Program   Associate Professor

    2020.4

  • Kagoshima University   Research Field in Science, Science and Engineering Area Graduate School of Science and Engineering (Science) Mathematics and Computer Science Course   Associate Professor

    2014.4 - 2020.3

  •   多元数理科学研究科   助教

    2009.1 - 2014.3

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    Country:Japan

Professional Memberships

  • 日本数学会

    2004.4

 

Papers

  • 松本 詔 .  対称群のスピン表現に対するStanley指標公式 (表現論とその組合せ論的側面) .  数理解析研究所講究録 ( 2161 ) 58 - 72   2020.6

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    Language:Japanese   Publisher:京都大学数理解析研究所  

  • Sho Matsumoto, Piotr Śniady .  Linear versus spin: representation theory of the symmetric groups .  Algebraic Combinatorics3 ( 1 ) 249 - 280   2020.2Linear versus spin: representation theory of the symmetric groupsReviewed

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.5802/alco.92

  • Sho Matsumoto, Piotr Śniady .  Random strict partitions and random shifted tableaux .  Selecta Mathematica 26 ( 10 )   2020.1Random strict partitions and random shifted tableauxReviewed

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  • 松本 詔 .  対称群のスピン表現に対するKerov多項式 (組合せ論的表現論の諸相) .  数理解析研究所講究録 ( 2127 ) 50 - 65   2019.9

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    Language:Japanese   Publisher:京都大学数理解析研究所  

  • Sho Matsumoto .  A spin analogue of Kerov polynomials .  Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)14   2018A spin analogue of Kerov polynomialsReviewed

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)  

    Kerov polynomials describe normalized irreducible characters of the symmetric groups in terms of the free cumulants associated with Young diagrams. We suggest well- suited counterparts of the Kerov polynomials in spin (or projective) representation settings. We show that spin analogues of irreducible characters are polynomials in even free cumulants associated with double diagrams of strict partitions. Moreover, we present a conjecture for the positivity of their coefficients.

    DOI: 10.3842/SIGMA.2018.053

  • Matsumoto Sho .  Polynomiality of Plancherel Averages on Strict Partitions (Combinatorics of Lie Type) .  RIMS Kokyuroku ( 2039 ) 59 - 78   2017.7

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    Language:Japanese   Publisher:Research Institute for Mathematical Sciences, Kyoto University  

  • Sho Matsumoto .  Polynomiality of shifted Plancherel averages and content evaluations .  Annales Mathématiques Blaise Pascal24 ( 1 ) 55 - 82   2017Reviewed

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    The shifted Plancherel measure is a natural probability measure on strict partitions. We prove a polynomiality property for the averages of the shifted Plancherel measure. As an application, we give alternative proofs of some content evaluation formulas, obtained by Han and Xiong very recently. Our main tool is factorial Schur $Q$-functions.

    DOI: 10.5802/ambp.364

  • Benoit Collins, Sho Matsumoto .  Weingarten calculus via orthogonality relations: new applications .  ALEA, Latin American Journal of Probability and Mathematical Statistics14   631 - 656   2017Reviewed

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  • Juan-Diego Urbina, Jack Kuipers, Sho Matsumoto, Quirin Hummel, Klaus Richter .  Multiparticle Correlations in Mesoscopic Scattering: Boson Sampling, Birthday Paradox, and Hong-Ou-Mandel Profiles .  Physical Review Letters116   2016.3Multiparticle Correlations in Mesoscopic Scattering: Boson Sampling, Birthday Paradox, and Hong-Ou-Mandel ProfilesReviewed

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1103/PhysRevLett.116.100401

  • Tiefeng Jiang and Sho Matsumoto .  Moments of traces of circular beta-ensembles .  the Annals of Probability43 ( 6 ) 3279 - 3336   2015Moments of traces of circular beta-ensemblesReviewed

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    Authorship:Lead author   Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1214/14-AOP960

  • Sho Matsumoto, Sanefumi Moriyama .  ABJ fractional brane from ABJM Wilson loop .  Journal of High Energy Physics ( 3 )   2014.3ABJ fractional brane from ABJM Wilson loopReviewed

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  • Benoit Collins, Sho Matsumoto, Nadia Saad .  Integration of invariant matrices and moments of inverses of Ginibre and Wishart matrices .  Journal of Multivariate Analysis126   1 - 13   2014.1Integration of invariant matrices and moments of inverses of Ginibre and Wishart matricesReviewed

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  • Sho Matsumoto .  Weingarten calculus for matrix ensembles associated with compact symmetric spaces .  Random Matrices: Theory and Applications2 ( 2 )   2013Weingarten calculus for matrix ensembles associated with compact symmetric spacesReviewed

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  • Sho Matsumoto, Jonathan Novak .  Jucys-Murphy elements and unitary matrix integrals .  International Mathematics Research Notices ( 2 ) 362 - 397   2013Jucys-Murphy elements and unitary matrix integralsReviewed

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  • Sho Matsumoto .  Moments of a single entry of circular orthogonal ensembles and Weingarten calculus .  Letters in Mathematical Physics103   113 - 130   2013Moments of a single entry of circular orthogonal ensembles and Weingarten calculus Reviewed

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  • Sho Matsumoto, Tomoyuki Shirai .  Correlation functions for zeros of a Gaussian power series and Pfaffians .  Electronic Journal of Probability18 ( 49 ) 1 - 18   2013Correlation functions for zeros of a Gaussian power series and PfaffiansReviewed

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  • Sho Matsumoto .  General moments of matrix elements from circular orthogonal ensembles .  Random Matrices: Theory and Applications1 ( 3 )   2012General moments of matrix elements from circular orthogonal ensemblesReviewed

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  • Sho Matsumoto .  General moments of the inverse real Wishart distribution and orthogonal Weingarten functions .  Journal of Theoretical Probability 25 ( 3 ) 798 - 822   2012General moments of the inverse real Wishart distribution and orthogonal Weingarten functionsReviewed

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  • Sho Matsumoto .  Jucys-Murphy elements, orthogonal matrix integrals, and Jack measures .  The Ramanujan Journal26 ( 1 ) 69 - 107   2011Jucys-Murphy elements, orthogonal matrix integrals, and Jack measuresReviewed

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  • Sho Matsumoto .  Moments of characteristic polynomials of a random matrix associated with compact symmetric spaces .  Infinite dimensional harmonic analysis IV, World Sci. Publ., Hackensack, NJ   196 - 208   2009Moments of characteristic polynomials of a random matrix associated with compact symmetric spacesReviewed

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    Language:English   Publishing type:Research paper (international conference proceedings)  

  • Kazufumi Kimoto, Sho Matsumoto, Masato Wakayama .  Alpha-determinant cyclic modules and Jacobi polynomials .  Transactions of the American Mathematical Society361 ( 12 ) 6447 - 6473   2009Alpha-determinant cyclic modules and Jacobi polynomialsReviewed

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    Language:English   Publishing type:Research paper (scientific journal)  

  • Benoit Collins, Sho Matsumoto .  On some properties of orthogonal Weingarten functions .  Journal of Mathematical Physics50 ( 11 )   2009On some properties of orthogonal Weingarten functionsReviewed

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  • Sho Matsumoto .  Jack deformations of Plancherel measures and traceless Gaussian random matrices .  Electronic Journal of Combinatorics15 ( 1 )   2008Jack deformations of Plancherel measures and traceless Gaussian random matrices Reviewed

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  • Sho Matsumoto .  Hyperdeterminantal expressions for Jack functions of rectangular shapes .  Journal of Algebra320 ( 2 ) 612 - 632   2008Hyperdeterminantal expressions for Jack functions of rectangular shapesReviewed

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  • Sho Matsumoto .  Moments of characteristic polynomials for compact symmetric spaces and Jack polynomials .  Journal of Physics A40 ( 45 ) 13567 - 13586   2007Moments of characteristic polynomials for compact symmetric spaces and Jack polynomialsReviewed

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  • Sho Matsumoto, Masato Wakayama .  Alpha-determinant cyclic modules of gln(C) .  Journal of Lie Theory16 ( 2 ) 393 - 405   2006Alpha-determinant cyclic modules of gln(C)Reviewed

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  • Sho Matsumoto .  Alpha-Pfaffian, Pfaffian point process and shifted Schur measure .  Linear Algebra and its Applications403   369 - 398   2005Alpha-Pfaffian, Pfaffian point process and shifted Schur measureReviewed

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  • Kazufumi Kimoto, Nobushige Kurokawa, Sho Matsumoto, Masato Wakayama .  Multiple finite Riemann zeta functions .  Acta Arithmetica116 ( 2 ) 173 - 187   2005Multiple finite Riemann zeta functionsReviewed

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  • Sho Matsumoto .  A scaling limit for t-Schur measures .  Kyushu Journal of Mathematics59 ( 1 ) 25 - 38   2005A scaling limit for t-Schur measuresReviewed

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  • Sho Matsumoto .  Correlation functions of the shifted Schur measure .  Journal of the Mathematical Society of Japan57 ( 3 ) 619 - 637   2005Correlation functions of the shifted Schur measureReviewed

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Presentations

  • 松本詔   ほぼ正方形のヤング図形に対応する対称群の正規化指標   International coauthorship

    第2回 分布族・離散集合の幾何学とその周辺  2021.3 

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    Event date: 2021.3

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:オンライン   Country:Japan  

  • 松本詔   対称群のスピン指標のStanley指標公式   Invited

    JCCA2020-DMIA2020-SGT9 

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    Event date: 2020.8

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:オンライン  

  • 松本 詔   対称群のスピン表現に対するStanley指標公式   International conference

    RIMS共同研究(公開型)「表現論とその組合せ的側面」 

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    Event date: 2019.10

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:京都大学数理解析研究所  

  • Sho Matsumoto   Kerov polynomials and Stanley formulas for spin symmetric groups   International conference

    Interactions between commutative and non-commutative probability 

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    Event date: 2019.8

    Language:English   Presentation type:Oral presentation (general)  

    Venue:京都大学  

  • 松本 詔   Kerov多項式とStanley指標公式  

    可換確率論と非可換確率論の相互作用準備会 

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    Event date: 2019.4

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:名古屋大学  

  • Sho Matsumoto   Weingarten calculus for random matrices associated with the compact symmetric space of class D III   International conference

    Workshop on "Random Matrices and Related Topics" 

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    Event date: 2019.2

    Language:English   Presentation type:Oral presentation (general)  

    Venue:東北大学  

  • 松本詔   対称群のスピン表現に対するKerov多項式  

    RIMS共同研究(公開型)「組合せ論的表現論の諸相」 

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    Event date: 2018.10

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:京都大学数理解析研究所  

    対称群の既約指標を正規化したものは, 自由キュムラントを変数とする多 項式で表すことができる. この多項式は Kerov 多項式と呼ばれ, 対称群の漸近的表現論におい て重要な役割を果たす. ここで自由キュムラントとは自由確率論の用語だが, Young 図形から 定まる推移測度のモーメントを通じて定義される量である. Kerov 多項式の係数はすべて非負 整数であることが Kerov 自身により予想され, F ́eray(2009) により証明された. 本講演では対 称群のスピン既約指標に対し, 対応する「スピン Kerov 多項式」をどのように定めるべきかを 考察し, Kerov 予想のスピン版を提示する. arXiv:1803.01121.

  • 松本詔   直交群の Weingarten calculus と Weingarten グラフ   Invited

    2018年度(第57回)実函数論・函数解析学合同シンポジウム 

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    Event date: 2018.9

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Venue:拓殖大学  

  • Sho Matsumoto   Weingarten calculus and counting paths on Weingarten graphs   Invited International conference

    Random matrices and their applications 

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    Event date: 2018.5

    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:京都大学  

  • 松本詔   Weingarten calculus for Haar distributed matrices and Wishart matrices   Invited

    確率・統計・行列ワークショップ松本2017 

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    Event date: 2017.11

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:信州大学  

  • 松本詔   Introduction to Weingarten calculus via orthogonal relations  

    ワークショップ「行列解析の展開」 

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    Event date: 2017.3

    Language:English   Presentation type:Oral presentation (general)  

    Venue:名古屋大学多元数理科学研究科  

  • Sho Matsumoto   Plancherel measures on strict partitions: Polynomiality and limit shape problems   Invited International conference

    Workshop on Asymptotic Reprensentation Theory 

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    Event date: 2017.2

    Language:English   Presentation type:Oral presentation (invited, special)  

    Venue:Institut Henri Poincare  

  • 松本詔   Polynomiality of Plancherel averages on strict partitions  

    RIMS集会「リー型の組合せ論」 

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    Event date: 2016.10

    Language:English   Presentation type:Oral presentation (general)  

    Venue:京都大学数理解析研究所  

  • 松本詔   Polynomiality of Plancherel averages on strict partitions  

    表現論がつなぐ数学 2016 

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    Event date: 2016.9

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:沖縄県那覇市  

  • 松本詔   マップの数え上げによるSchwinger-Dyson 方程式の解の構成  

    鹿児島解析・確率論セミナー 

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    Event date: 2016.8

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:鹿児島大学  

  • 松本詔   ランダム行列とマップの数え上げ  

    第1回「Free Monotone Transport」を読む会 

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    Event date: 2016.3

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:成田ビューホテル  

  • 松本詔   ランダム行列と順列の数え上げ  

    Kunitachi One-Day Symposium on the Recent Developments in the Mathematical Science 

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    Event date: 2016.2

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:一橋大学  

  • 松本詔   SU(n)のWeingarten calculusへ向けて  

    表現論がつなぐ数学2015  松本詔

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    Event date: 2015.9

    Language:Japanese   Presentation type:Oral presentation (general)  

    Venue:JR九州ホテル鹿児島  

  • 松本詔   Weingarten calculus と 対称群の調和解析   Invited

    日本数学会2015年度秋季総合分科会  日本数学会

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    Event date: 2015.9

    Language:Japanese   Presentation type:Oral presentation (invited, special)  

    Venue:京都産業大学  

  • 松本詔   円βアンサンブルの中心極限定理とJack多項式  

    第10回代数・解析・幾何セミナー  第10回代数・解析・幾何セミナー

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    Event date: 2015.2

    Language:Japanese  

    Venue:鹿児島  

    研究会

  • 松本詔   円βアンサンブルのトレースの中心極限定理  

    確率論シンポジウム  確率論シンポジウム

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    Event date: 2014.12

    Language:Japanese  

    Venue:京都  

    研究会

  • 松本詔   Central limit theorems for traces in circular beta-ensembles  

    Zeta Functions in OKINAWA 2014  Zeta Functions in OKINAWA 2014

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    Event date: 2014.10

    Language:Japanese  

    Venue:沖縄  

    研究会

  • 松本詔   ランダム行列の行列成分と組合せ論  

    第192回数理情報科学談話会  第192回数理情報科学談話会

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    Event date: 2014.4

    Language:Japanese  

    Venue:鹿児島  

    研究会

  • 松本詔   コンパクト対称空間に付随する行列空間上の多項式積分について  

    RIMS研究集会「組合せ論的表現論の展望」  RIMS研究集会「組合せ論的表現論の展望」

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    Event date: 2013.10

    Language:Japanese  

    Venue:京都  

    研究会

  • 松本詔   例外型コンパクトLie群G2上のWeingarten calculus  

    研究集会「Zeta Functions in OKINAWA 2013」  研究集会「Zeta Functions in OKINAWA 2013」

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    Event date: 2013.10

    Language:Japanese  

    Venue:沖縄  

    研究会

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Research Projects

  • 組合せ論と表現論に基づく、ランダム分割とランダム行列の研究

    2017.4

    科学研究費補助金  基盤研究(C)

  • 表現論,ランダム行列とその周辺の研究

    2013.4 - 2017.3

    科学研究費補助金  若手研究(B)