OKADO Masato

写真a

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Title

Professor

Laboratory location

Sugimoto Campus

Degree 【 display / non-display

  • Kyoto University -  Doctor of Science

Research Areas 【 display / non-display

Algebra

Current Career 【 display / non-display

  • Osaka City University   Graduate School of Science   Mathematics and Physics Course   Professor  

Graduate School 【 display / non-display

  •  
     
     

    Kyoto University  Graduate School, Division of Natural Science 

Graduating School 【 display / non-display

  •  
     
     

    The University of Tokyo   Faculty of Liberal Arts  

 

Published Papers 【 display / non-display

  • Kirillov-Reshetikhin modules of generalized quantum groups of Type A

    Jae-Hoon Kwon, Masato Okado

    Publications of the Research Institute for Mathematical Sciences  57   993 - 1039 2021.09  [Refereed]  [Invited]

  • Higher Level q-Oscillator Representations for U-q(C-n((1))), U-q(C-(2)(n+1)) and U-q(B-(1)(0, n))

    Kwon Jae-Hoon, Okado Masato

    COMMUNICATIONS IN MATHEMATICAL PHYSICS  2021.02  [Refereed]

    DOI

  • Set-theoretical solutions to the reflection equation associated to the quantum affine algebra of type $A^{(1)}_{n-1}$

    Atsuo Kuniba, Masato Okado

    Journal of Integrable Systems  4 ( 1 ) xyz013 - (10 pages) 2019.12  [Refereed]

  • Reflection K matrices associated with an Onsager coideal of U-p(A(n-1)((1))), U-p(B-n((1))), U-p(D-n((1))) and U-p(D-n+1((2)))

    Kuniba Atsuo, Okado Masato, Yoneyama Akihito

    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL  52 ( 37 )  2019.09  [Refereed]

    DOI

  • Matrix product solution to the reflection equation associated with a coideal subalgebra of Uq(An-1(1))

    Kuniba Atsuo, Okado Masato, Yoneyama Akihito

    LETTERS IN MATHEMATICAL PHYSICS  109 ( 9 ) 2049 - 2067 2019.09  [Refereed]

    DOI

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Books etc 【 display / non-display

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Review Papers (Misc) 【 display / non-display

  • Energy Functions in Box Ball Systems

    OKADO Masato

    International Journal of Modern Physics A  15   1379 2000  [Refereed]  [Invited]

    DOI

  • Finite Crystals and Paths(共著)

    OKADO Masato

    Advanced Studies in Pure Mathematics  28   115 2000  [Refereed]  [Invited]

  • Branching Functions of An-1 and Jantzen-Seitz Problem for Ariki-Koike Algebras(共著)

    OKADO Masato

    Advances in Mathematics  141   322 1999  [Refereed]  [Invited]

  • Remarks on Fermionic Formula(共著)

    OKADO Masato

    Contemporary Mathematics  248   243 1999  [Refereed]  [Invited]

  • Character Formulae of ┣DAsl(/)∧┫DAn-Modules and Inhomogeneous Paths(共著)

    OKADO Masato

    Nuclear Physics  B536[PM]   575 1998  [Refereed]  [Invited]

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Conference Activities & Talks 【 display / non-display

  • Quantum super duality

    Masato Okado  [Invited]

    RIMS研究集会 Representation theory of algebraic groups and quantum groups  2019.10 

  • Integrable systems arising from Kirillov-Reshetikhin crystals of quantum affine algebras

    Masato Okado  [Invited]

    SIDE 13  2018.11 

  • Generalized quantum groups and fusion procedure

    Masato Okado  [Invited]

    MATRIX program ``Non-Equilibrium Systems and Special Functions"  2018.01 

  • Integrable stochastic models and quantum groups

    M. Okado  [Invited]

    Frontiers in Mathematical Physics  2017.01 

  • Similarity of Kirillov-Reshetikhin crystals and its applications

    M. Okado  [Invited]

    ICM 2014 Satellite Conference on Representation Theory and Related Topics  2014.09 

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Grant-in-Aid for Scientific Research 【 display / non-display

  • Studies of the algebraic and combinatorial structures related to quantum integrable systems

    Project/Area Number : 23340007  Grant-in-Aid for Scientific Research(B) Representative

    Project Year :

    2011.04
    -
    2016.03
     

    Partaker : KUNIBA Atsuo, NAKANISHI Tomoki, YAMADA Yasuhiko, SCHILLING Anne

     View Summary

    Principal investigator Okado constructed, with Schilling and Sakamoto, a bijection between highest weight paths and rigged configurations for type D in full generality, and thereby settled the X=M conjecture in a combinatorial way. Nakanishi studied, with his collaborators, the cluster algebra from the aspect of quantum integrable systems and clarified the periodicity, dilogarithm identities, the relation between exact WKB analysis and mutation, etc. Although it was not included in the purposes of this project in the beginning of the project period, Kuniba started the study of 3-dimensional quantum integrable systems. Later, together with Okado and other collaborators, he produced results, such as the relation between quantum coordinate rings and PBW bases, 2-dimensional reduction of the tetrahedron equation, applications to Markovian processes.

  • Approach to the polynomials related to representation theory from quantum integrable systems

    Project/Area Number : 23654007  Grant-in-Aid for challenging Exploratory Research Representative

    Project Year :

    2011
    -
    2013
     

    Partaker : KUNIBA Atsuo, YAMADA Yasuhiko, SAKAMOTO Reiho, SCHILLING Anne

     View Summary

    The study of X=M conjecture, which originates in quantum integrable systems, equating the generating functions of highest weight elements of the tensor product of KR crystals and rigged configurations has advanced about 80% to the goal for type D. Research for the exceptional case E6 was also begun. However, the study of the relation to LLT polynomial remained to be incomplete.
    We also studied the relation between tetrahedron equation and quantum groups, namely, explicit formula for the solution to the 3D reflection equation, relation between matrix elements of the intertwiner of the quantum coordinate ring and PBW bases of the quantum enveloping algebra, coincidence of the 2D reduction and the intertwiner of the tensor product of q-oscillator representations of a quantum affine algebra.

  • Representation Theory of Quantum Groups and Integrable Systems

    Project/Area Number : 20540016  Grant-in-Aid for Scientific Research(C) Representative

    Project Year :

    2008
    -
    2010
     

    Partaker : NOBE Atsushi, SAKAMOTO Reiho, NAKASHIMA Toshiki, FOURIER Ghislain, LECOUVER Cedric, MISRA Kailash C., SCHILLING Anne, SHIMOZONO Mark

     View Summary

    We proved the existence of the crystal bases in the sense of Kashiwara for KR modules of the quantum groups of nonexceptional affine type, and determined their crystal structure. We then settled affirmatively the conjecture on the perfectness of KR crystals. By examining the combinatorial structure of the KR crystal, we solved the X=K conjecture by Shimozono-Zabrocki. On the other hand, we showed that a similar relation holds for the generating functions of rigged configurations, thereby solving the X=M conjecture for all nonexceptional affine types when the rank is sufficiently large.

  • Ultradiscrete solitons and solvable lattice models

    Project/Area Number : 19540393  Grant-in-Aid for Scientific Research(C) Representative

    Project Year :

    2007
    -
    2008
     

    Partaker : OKADO Masato

  • Integrable Systems and Combinatorial Representation Theory

    Project/Area Number : 18540030  Grant-in-Aid for Scientific Research(C) Representative

    Project Year :

    2006
    -
    2007
     

    Partaker : YAMADA Yasuhiko, KUNIBA Atsuo, NOBE Atsushi

     View Summary

    During the period of research project, we mainly obtained the following results.
    1. [Affine geometric crystal]
    In collaboration with M. Kashiwara and T. Nakashima, we constructed geometric crystals associated to nonexceptional affine Lie algebras. We confirmed that the ultra-discrete limit of these geometric crystals coincide with the limit of previously known perfect crystals. Moreover, except type C, we obtained explicit formulas for birational maps, called tropical R maps, that satisfy the Yang-Baxter equation.
    2. [Existence of crystal bases of the KR modules for nonexceptional types]
    There was a conjecture saying that any finite-dimensional representation of a quantum affirm algebra that has an integer multiple of a level 0 fundamental weight as highest weight (KR module) has a crystal base. We solved this conjecture for all affine Lie algebras of nonexceptional types. In collaboration with A. Schilling, we also proved that the crystals of type B^<(1)>_n, D^<(1)>_n, and A^<(2)>_<2n-1> are isomorphic to the combinatorial crystals recently constructed by Schilling.
    3. [Construction of the coherent family of perfect crystals for exceptional types]
    In collaboration with M. Kashiwara, K.C. Misra and D. Yamada, we revealed the crystal structure of the perfect crystals associated to the exceptional affine lie algebra D^<(3)>_4 at any level.

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Other educational activity and Special note 【 display / non-display

  • Class teacher

    (2019)

  • Class teacher

    (2018)

  • Class teacher

    (2017)

 

Foreigner acceptance 【 display / non-display

  • Academic year : 2019

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    Number of foreigners accepted
    2

    米、韓国

  • Academic year : 2018

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    Number of foreigners accepted
    3

    米、豪、韓国

  • Academic year : 2017

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    Number of foreigners accepted
    5

    米、豪、韓国