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2022 Fiscal Year Annual Research Report

Supersymmetric rigged configurations and crystals of quantum affine supergroups

Research Project

Project/Area Number 21F51028
Research InstitutionOsaka Metropolitan University

Principal Investigator

尾角 正人  大阪公立大学, 大学院理学研究科, 教授 (70221843)

Co-Investigator(Kenkyū-buntansha) SCRIMSHAW TRAVIS  大阪公立大学, 大学院理学研究科, 外国人特別研究員
Project Period (FY) 2021-11-18 – 2024-03-31
KeywordsCrystal basis / Lie superalgebra / skew Howe duality
Outline of Annual Research Achievements

In addition to 2 papers on combinatorial representation theory being published, an additional 4 papers appeared on the arXiv preprint server, as follows.
I authored a paper on cellular subalgebras of the partition algebra. We described various diagram algebras and their representation theory using cellular algebras of Graham and Lehrer and the decomposition into half diagrams. We gave a new construction to build new cellular algebras from a general cellular algebra and subalgebras of the rook Brauer algebra that we call the cellular wreath product.
I coauthored a paper on a generalized definition for the quantum Clifford algebra introduced by Hayashi in 1990 using another parameter k that we call the twist, which was essential for my coauthor's subsequent work on quantum skew Howe duality and made a new connection with the alternative construction of Faddeev, Reshetikhin, and Takhtajan.
The second paper on rational lifting of crystal structures to study the ring of invariants was completed, building on our first paper from last year.
Lastly, the first of a series of at least 3 papers on the connection between Schubert calculus and stochastic particle processes was finished and uploaded.

Research Progress Status

翌年度、交付申請を辞退するため、記入しない。

Strategy for Future Research Activity

翌年度、交付申請を辞退するため、記入しない。

  • Research Products

    (9 results)

All 2022 Other

All Int'l Joint Research (3 results) Journal Article (2 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 2 results,  Open Access: 2 results) Presentation (4 results) (of which Int'l Joint Research: 4 results,  Invited: 4 results)

  • [Int'l Joint Research] Stanford University/University of Minnesota(米国)

    • Country Name
      U.S.A.
    • Counterpart Institution
      Stanford University/University of Minnesota
  • [Int'l Joint Research] Universite du Quebec a Montreal(カナダ)

    • Country Name
      CANADA
    • Counterpart Institution
      Universite du Quebec a Montreal
  • [Int'l Joint Research] St. Petersburg State University(ロシア連邦)

    • Country Name
      RUSSIA FEDERATION
    • Counterpart Institution
      St. Petersburg State University
  • [Journal Article] Quasi-solvable lattice models for Sp_{2n} and SO_{2n+1} Demazure atoms and characters2022

    • Author(s)
      Valentin Buciumas, Travis Scrimshaw
    • Journal Title

      Forum Math. Sigma

      Volume: 10 Pages: e53

    • DOI

      10.1017/fms.2022.49

    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Candidate for the crystal B(-∞) for the queer Lie superalgebra2022

    • Author(s)
      Ben Salisbury, Travis Scrimshaw
    • Journal Title

      Kyoto J. Math.

      Volume: 62 Pages: 377-401

    • DOI

      10.1215/21562261-2022-0010

    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Presentation] Crystal Invariant Theory2022

    • Author(s)
      Travis Scrimshaw
    • Organizer
      Seoul National University
    • Int'l Joint Research / Invited
  • [Presentation] Rational liftings and gRSK2022

    • Author(s)
      Travis Scrimshaw
    • Organizer
      Seoul National University
    • Int'l Joint Research / Invited
  • [Presentation] Crystal Invariant Theory2022

    • Author(s)
      Travis Scrimshaw
    • Organizer
      CAGE Seminar, Drexel University
    • Int'l Joint Research / Invited
  • [Presentation] Representation theory of the quantum Clifford algebra2022

    • Author(s)
      Travis Scrimshaw
    • Organizer
      Conference of Algebraic Representation Theory 2022, Tsukuba University
    • Int'l Joint Research / Invited

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Published: 2023-12-25  

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