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Representation Theory, Geometry and Combinatorics Associated to Springer Fibers
Representation Theory, Geometry and Combinatorics Associated to Springer Fibers
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202103023
- ISBN
- 9798286435517
- DDC
- 510
- 저자명
- Hoang, Do Kien.
- 서명/저자
- Representation Theory, Geometry and Combinatorics Associated to Springer Fibers
- 발행사항
- [Sl] : Yale University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 228 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
- 주기사항
- Advisor: Loseu, Ivan.
- 학위논문주기
- Thesis (Ph.D.)--Yale University, 2025.
- 초록/해제
- 요약This dissertation explores various aspects of Springer fibers and their deep connections to geometric and combinatorial representation theory. It combines the works of [H24a], [H24b], and [H24c] by the author during his PhD. Throughout these works, we explain sophisticated roles of Springer fibers in modern topics like modular representation theory and symplectic duality. Additionally, we resolve several classical questions concerning the Springer correspondence and the cohomology of Springer fibers.The first project centers around a discretization of a Springer fiber Be. This discretization is a finite set Ye that has appeared in various contexts in representation theory. A key theme of our result is that Ye also discretizes a distinguished fixed-point variety Bgre ⊂ Be. For certain families of Springer fibers, we describe Ye explicitly using full exceptional collections in Db (Coh(Bgre)). This perspective provides a novel categorical model for the discretization.The second project studies the action of a finite group on the irreducible components of Be. We obtain an explicit classification of stabilizers in this action, proving a conjecture of Lusztig and Sommers. This suggests an unexplored connection between Springer fibers, component group actions, and Kazhdan-Lusztig cells in finite Weyl groups.The third project focuses on the Hikita conjecture for nilpotent orbits, which predicts a graded isomorphism between the cohomology of a Springer fiber and the ring of functions on the scheme-theoretic intersection of a nilpotent orbit closure with a Cartan subalgebra. We provide an almost complete classification of cases where this isomorphism holds by analyzing cohomological surjectivity and flatness conditions.
- 일반주제명
- Mathematics
- 일반주제명
- Theoretical mathematics
- 일반주제명
- Applied mathematics
- 키워드
- Cohomology
- 키워드
- Springer fibers
- 기타저자
- Yale University Mathematics
- 기본자료저록
- Dissertations Abstracts International. 86-12B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■006m o d
■007cr#unu||||||||
■020 ▼a9798286435517
■035 ▼a(MiAaPQ)AAI31844861
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aHoang, Do Kien.
■24510▼aRepresentation Theory, Geometry and Combinatorics Associated to Springer Fibers
■260 ▼a[Sl]▼bYale University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a228 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-12, Section: B.
■500 ▼aAdvisor: Loseu, Ivan.
■5021 ▼aThesis (Ph.D.)--Yale University, 2025.
■520 ▼aThis dissertation explores various aspects of Springer fibers and their deep connections to geometric and combinatorial representation theory. It combines the works of [H24a], [H24b], and [H24c] by the author during his PhD. Throughout these works, we explain sophisticated roles of Springer fibers in modern topics like modular representation theory and symplectic duality. Additionally, we resolve several classical questions concerning the Springer correspondence and the cohomology of Springer fibers.The first project centers around a discretization of a Springer fiber Be. This discretization is a finite set Ye that has appeared in various contexts in representation theory. A key theme of our result is that Ye also discretizes a distinguished fixed-point variety Bgre ⊂ Be. For certain families of Springer fibers, we describe Ye explicitly using full exceptional collections in Db (Coh(Bgre)). This perspective provides a novel categorical model for the discretization.The second project studies the action of a finite group on the irreducible components of Be. We obtain an explicit classification of stabilizers in this action, proving a conjecture of Lusztig and Sommers. This suggests an unexplored connection between Springer fibers, component group actions, and Kazhdan-Lusztig cells in finite Weyl groups.The third project focuses on the Hikita conjecture for nilpotent orbits, which predicts a graded isomorphism between the cohomology of a Springer fiber and the ring of functions on the scheme-theoretic intersection of a nilpotent orbit closure with a Cartan subalgebra. We provide an almost complete classification of cases where this isomorphism holds by analyzing cohomological surjectivity and flatness conditions.
■590 ▼aSchool code: 0265.
■650 4▼aMathematics
■650 4▼aTheoretical mathematics
■650 4▼aApplied mathematics
■653 ▼aCohomology
■653 ▼aExceptional collection
■653 ▼aHikita conjecture
■653 ▼aKazhdan-Lusztig theory
■653 ▼aSpringer correspondence
■653 ▼aSpringer fibers
■690 ▼a0405
■690 ▼a0642
■690 ▼a0364
■71020▼aYale University▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g86-12B.
■790 ▼a0265
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17356719▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
