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Supersingular representations of p-adic groups

Research Project

Project/Area Number 18K18707
Research Category

Grant-in-Aid for Challenging Research (Exploratory)

Allocation TypeMulti-year Fund
Review Section Medium-sized Section 11:Algebra, geometry, and related fields
Research InstitutionThe University of Tokyo

Principal Investigator

Abe Noriyuki  東京大学, 大学院数理科学研究科, 准教授 (00553629)

Project Period (FY) 2018-06-29 – 2022-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥6,370,000 (Direct Cost: ¥4,900,000、Indirect Cost: ¥1,470,000)
Fiscal Year 2020: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2019: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2018: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Keywords超特異表現 / 簡約群 / p進群 / p進簡約群
Outline of Final Research Achievements

Langlands correspondence is one of the most important problems in number theory. The aim of this project is, by studying modulo p representations of reductive groups, to make a contribution to Langlands correspondence, especially modulo p Langlands correspondence. Among modulo p representations, a class called supersingular representations are still mysterious and I tried to study such representations, I got some results on algebraic representations of reductive groups which is important to study supersingular representations.

Academic Significance and Societal Importance of the Research Achievements

Langlands対応は整数論に始まり,表現論や数理物理など多くの分野と関連し現在では巨大な理論として多くの研究者により研究が行われてきている.また,簡約群の代数的な表現論も近年急速な発展を見せており,注目されている理論である.本研究はこれらの理論,特に後者に対して,主に組み合わせ論的な側面から新たな知見を与えることができた.関連する研究が他の研究者により行われたことを考えても,一定の学術的意義のある結果を得ることができた.

Report

(5 results)
  • 2021 Annual Research Report   Final Research Report ( PDF )
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (7 results)

All 2021 2020 2019

All Journal Article (2 results) (of which Peer Reviewed: 2 results,  Open Access: 1 results) Presentation (5 results) (of which Int'l Joint Research: 2 results,  Invited: 3 results)

  • [Journal Article] A bimodule description of the Hecke category2021

    • Author(s)
      Noriyuki Abe
    • Journal Title

      Compositio Mathematica

      Volume: 157 Issue: 10 Pages: 2133-2159

    • DOI

      10.1112/s0010437x21007466

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A comparison between pro-p-Iwahori Hecke modules and mod p representations,2019

    • Author(s)
      Noriyuki Abe
    • Journal Title

      Algebra & Number Theory

      Volume: 13 Issue: 8 Pages: 1959-1981

    • DOI

      10.2140/ant.2019.13.1959

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] On Soergel bimodules2020

    • Author(s)
      Noriyuki Abe
    • Organizer
      Geometry and representation theory
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On Soergel bimodules2020

    • Author(s)
      Noriyuki Abe
    • Organizer
      第15回代数・解析・幾何学セミナー
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] On Soergel bimodules2019

    • Author(s)
      阿部紀行
    • Organizer
      2019年度RIMS共同研究(公開型) 「表現論とその周辺分野の進展」
    • Related Report
      2019 Research-status Report
  • [Presentation] A Hecke action on G1TG_1T-modules,2019

    • Author(s)
      Noriyuki Abe
    • Organizer
      Modular Representation Theory
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On Soergel bimodules2019

    • Author(s)
      阿部紀行
    • Organizer
      Arithmetic Geometry and Representation Theory
    • Related Report
      2019 Research-status Report

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Published: 2018-07-25   Modified: 2023-01-30  

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