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2022 年度 実績報告書

Cyclotomic KLR algebras in type C: cellularity and blocks

研究課題

研究課題/領域番号 20K22316
研究機関沖縄科学技術大学院大学

研究代表者

Speyer Liron  沖縄科学技術大学院大学, 表現論と代数的組合せ論ユニット, 准教授(Assistant Professor) (00873762)

研究期間 (年度) 2020-09-11 – 2023-03-31
キーワードCellular algebras / Quiver Hecke algebras / Representation theory / KLR algebras / Specht modules
研究実績の概要

During the course of this project, Andrew Mathas and Anton Evseev released a proof of cellularity for the type C cyclotomic KLR algebras. We have redirected our efforts into related structural questions for type C KLR algebras. We have almost completed a paper, joint with Chris Chung and Andrew Mathas, in which we determine graded decomposition matrices for small rank level 1 cyclotomic KLR algebras in type C, as well as the structures of many Specht modules. We have another ongoing project studying arbitrary cyclotomic quotients in finite type C in further detail.
Our joint work with Susumu Ariki last year showed that all weight 2 and weight 3 blocks of type A Hecke algebras are Schurian-infinite, along with several families of blocks of larger weight. This year, we extended this with Sinead Lyle to prove that all blocks of weight at least 2 are Schurian-infinite.
Finally, I have supervised PhD students working on projects relating to type C KLR algebras, too. My student Berta Hudak, together with my postdoc Chris Chung, has recently completed a preprint in which the representation type of all level 1 cyclotomic KLR algebras in type C are determined, generalising results of Ariki and Park. My other student Martin Forsberg Conde is working on homomorphisms between Specht modules in type C, in particular aiming to prove a Carter-Payne type theorem there.

Besides research done for the proposed project, I have been running a fortnightly representation theory seminar over Zoom, bringing in speakers and an audience from several countries.

  • 研究成果

    (9件)

すべて 2022 その他

すべて 国際共同研究 (4件) 学会発表 (5件) (うち国際学会 1件、 招待講演 4件)

  • [国際共同研究] University of East Anglia(英国)

    • 国名
      英国
    • 外国機関名
      University of East Anglia
  • [国際共同研究] Washington & Jefferson College(米国)

    • 国名
      米国
    • 外国機関名
      Washington & Jefferson College
  • [国際共同研究] University of Sydney(オーストラリア)

    • 国名
      オーストラリア
    • 外国機関名
      University of Sydney
  • [国際共同研究] Osaka University(日本)

    • 国名
      日本
    • 外国機関名
      Osaka University
  • [学会発表] Schurian-infinite blocks of type A Hecke algebras2022

    • 著者名/発表者名
      Liron Speyer
    • 学会等名
      York Algebra Seminar
    • 招待講演
  • [学会発表] Schurian-infinite blocks of type A Hecke algebras2022

    • 著者名/発表者名
      Liron Speyer
    • 学会等名
      Conference on Algebraic Representation Theory 2022
    • 招待講演
  • [学会発表] Schurian-infinite blocks of type A Hecke algebras2022

    • 著者名/発表者名
      Liron Speyer
    • 学会等名
      MSJ Autumn Meeting 2022
    • 国際学会
  • [学会発表] The representation theory of type A Iwahori-Hecke algebras II2022

    • 著者名/発表者名
      Liron Speyer
    • 学会等名
      Silver workshop V: Complex Geometry and related topics, OIST
    • 招待講演
  • [学会発表] Graded decomposition matrices for type C KLR algebras2022

    • 著者名/発表者名
      Liron Speyer
    • 学会等名
      Representation Theory, Combinatorics and Geometry, National University of Singapore
    • 招待講演

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公開日: 2023-12-25  

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