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Equivalence of Hecke Categories with Deeper Level Structures
Equivalence of Hecke Categories with Deeper Level Structures
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211151425
- ISBN
- 9798382777566
- DDC
- 510
- 저자명
- Xia, Jianqiao.
- 서명/저자
- Equivalence of Hecke Categories with Deeper Level Structures
- 발행사항
- [Sl] : Harvard University, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 95 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
- 주기사항
- Advisor: Yun, Zhiwei.
- 학위논문주기
- Thesis (Ph.D.)--Harvard University, 2024.
- 초록/해제
- 요약Let G be a reductive group of classical type. We study representations of the loop group G((t)) and geometrizations of Hecke algebras. The representations are generalizations of epipelagic representations. They have positive depth and appear in the representation induced from some level group (J, ψ). The associated Hecke category is the category of mixed Ql-sheaves on G((t)) with equivariant conditions, and we prove that this monoidal category is equivalent to an ane Hecke category of a smaller group H (not necessarily split). This equivalence relates certain positive depth representations of G((t)) and tamely ramified representations of H. Therefore, it has potential applications to local geometric Langlands program in a wildly ramified setting. The proof relies on the theory of Soergel bimodules and a reduction step using hyperbolic localization. It can be potentially generalized to (J, ψ) defined using Yu's data.
- 일반주제명
- Mathematics
- 일반주제명
- Theoretical mathematics
- 키워드
- Hecke category
- 기타저자
- Harvard University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 85-12B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■006m o d
■007cr#unu||||||||
■020 ▼a9798382777566
■035 ▼a(MiAaPQ)AAI31294631
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aXia, Jianqiao.▼0(orcid)0009-0008-7349-962X
■24510▼aEquivalence of Hecke Categories with Deeper Level Structures
■260 ▼a[Sl]▼bHarvard University▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a95 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 85-12, Section: B.
■500 ▼aAdvisor: Yun, Zhiwei.
■5021 ▼aThesis (Ph.D.)--Harvard University, 2024.
■520 ▼aLet G be a reductive group of classical type. We study representations of the loop group G((t)) and geometrizations of Hecke algebras. The representations are generalizations of epipelagic representations. They have positive depth and appear in the representation induced from some level group (J, ψ). The associated Hecke category is the category of mixed Ql-sheaves on G((t)) with equivariant conditions, and we prove that this monoidal category is equivalent to an ane Hecke category of a smaller group H (not necessarily split). This equivalence relates certain positive depth representations of G((t)) and tamely ramified representations of H. Therefore, it has potential applications to local geometric Langlands program in a wildly ramified setting. The proof relies on the theory of Soergel bimodules and a reduction step using hyperbolic localization. It can be potentially generalized to (J, ψ) defined using Yu's data.
■590 ▼aSchool code: 0084.
■650 4▼aMathematics
■650 4▼aTheoretical mathematics
■653 ▼aHecke category
■653 ▼aLanglands program
■653 ▼aRepresentation theory
■653 ▼aSoergel bimodules
■653 ▼aHyperbolic localization
■690 ▼a0405
■690 ▼a0642
■71020▼aHarvard University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g85-12B.
■790 ▼a0084
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17161646▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
