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Symplectic Duality for Hamiltonian Reductions; and Orthodontia for Double Grothendieck Polynomials
Symplectic Duality for Hamiltonian Reductions; and Orthodontia for Double Grothendieck Polynomials
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202104645
- ISBN
- 9798286452224
- DDC
- 510
- 서명/저자
- Symplectic Duality for Hamiltonian Reductions; and Orthodontia for Double Grothendieck Polynomials
- 발행사항
- [Sl] : The University of Chicago, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 95 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-01, Section: B.
- 주기사항
- Advisor: Ginzburg, Victor.
- 학위논문주기
- Thesis (Ph.D.)--The University of Chicago, 2025.
- 초록/해제
- 요약The Hamiltonian reduction N ///T of the nilpotent cone in sln by the torus of diagonal matrices is a Nakajima quiver variety which admits a symplectic resolution N///T, and the corresponding BFN Coulomb branch is the affine closure T∗(G/U) of the cotangent bundle of the base affine space. We construct a surjective map C [T ∗(G/U) TxB/U] ↠ H∗ [ N///T] of graded algebras, which the Hikita conjecture predicts to be an isomorphism. Our map is inherited from a related case of the Hikita conjecture and factors through Kirwan surjectivity for quiver varieties. We conjecture that many other Hikita maps can be inherited from that of a related dual pair.We give a new formula for double Grothendieck polynomials based on Magyar's orthodontia algorithm for diagrams. Our formula implies a similar formula for double Schubert polynomials Sw(x; y). We also prove a curious positivity result: for vexillary permutations w ∈ Sn, the polynomial xn1 . . . xnnSw(x−1n , . . . , x−11 ; 1, . . . , 1) is a graded nonnegative sum of Lascoux polynomials. We conjecture that this positivity result holds for all w ∈ Sn. This conjecture would follow from a problem of independent interest regarding Lascoux positivity of certain products of Lascoux polynomials.
- 일반주제명
- Mathematics
- 일반주제명
- Applied mathematics
- 키워드
- Isomorphism
- 기타저자
- The University of Chicago Mathematics
- 기본자료저록
- Dissertations Abstracts International. 87-01B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520260202104645
■006m o d
■007cr#unu||||||||
■020 ▼a9798286452224
■035 ▼a(MiAaPQ)AAI32114574
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aSetiabrata, Linus.
■24510▼aSymplectic Duality for Hamiltonian Reductions; and Orthodontia for Double Grothendieck Polynomials
■260 ▼a[Sl]▼bThe University of Chicago▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a95 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-01, Section: B.
■500 ▼aAdvisor: Ginzburg, Victor.
■5021 ▼aThesis (Ph.D.)--The University of Chicago, 2025.
■520 ▼aThe Hamiltonian reduction N ///T of the nilpotent cone in sln by the torus of diagonal matrices is a Nakajima quiver variety which admits a symplectic resolution N///T, and the corresponding BFN Coulomb branch is the affine closure T∗(G/U) of the cotangent bundle of the base affine space. We construct a surjective map C [T ∗(G/U) TxB/U] ↠ H∗ [ N///T] of graded algebras, which the Hikita conjecture predicts to be an isomorphism. Our map is inherited from a related case of the Hikita conjecture and factors through Kirwan surjectivity for quiver varieties. We conjecture that many other Hikita maps can be inherited from that of a related dual pair.We give a new formula for double Grothendieck polynomials based on Magyar's orthodontia algorithm for diagrams. Our formula implies a similar formula for double Schubert polynomials Sw(x; y). We also prove a curious positivity result: for vexillary permutations w ∈ Sn, the polynomial xn1 . . . xnnSw(x−1n , . . . , x−11 ; 1, . . . , 1) is a graded nonnegative sum of Lascoux polynomials. We conjecture that this positivity result holds for all w ∈ Sn. This conjecture would follow from a problem of independent interest regarding Lascoux positivity of certain products of Lascoux polynomials.
■590 ▼aSchool code: 0330.
■650 4▼aMathematics
■650 4▼aApplied mathematics
■653 ▼aGrothendieck polynomials
■653 ▼aSymplectic duality
■653 ▼aIsomorphism
■653 ▼aOrthodontia algorithm
■690 ▼a0405
■690 ▼a0364
■71020▼aThe University of Chicago▼bMathematics.
■7730 ▼tDissertations Abstracts International▼g87-01B.
■790 ▼a0330
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17358331▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
