상세정보
Export to Refworks부가기능
Affine Springer Fibers, Hilbert schemes and Knots
상세 프로파일
| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | Affine Springer Fibers, Hilbert schemes and Knots. |
| 개인저자 | Kivinen, Oscar Salomon. |
| 단체저자명 | University of California, Davis. Mathematics. |
| 발행사항 | [S.l.]: University of California, Davis., 2019. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2019. |
| 형태사항 | 105 p. |
| 기본자료 저록 | Dissertations Abstracts International 81-04B. Dissertation Abstract International |
| ISBN | 9781085796279 |
| 학위논문주기 | Thesis (Ph.D.)--University of California, Davis, 2019. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
Advisor: Gorskiy, Evgeny. |
| 이용제한사항 | This item must not be sold to any third party vendors.This item must not be added to any third party search indexes. |
| 요약 | Symmetry is abundant in mathematics, and often appears in the guise of representation theory. It often appears in unexpected places, and due to its highly structured nature can be a powerful tool in the study of other mathematical objects. This thesis is concerned with examples of such phenomena in the realm of geometric representation theory. More specifically, we study Hilbert schemes on singular plane curves and smooth surfaces as well as affine Springer fibers from various points of view in three stand-alone chapters, which are more interrelated than might seem to the untrained eye. In Chapter II, we relate Haiman's isospectral Hilbert scheme of points on the plane to certain very unramified elements in the loop Lie algebra of a split reductive group. These elements have already been studied in the work of Goresky, Kottwitz, and MacPherson. This novel connection proves a special case of a conjecture by Bezrukavnikov. In Chapter III, we study a certain subalgebra of the Weyl algebra on 2m variables acting on the homology of Hilbert schemes of points of a reduced complex planar curve with m irreducible components. We compute the representation in the fundamental example of the node and furthermore compute parts of the action in the case of m lines intersecting in the plane. A majority of the results in Chapters II-III are original. In Chapter IV, we study (geometric) representations of the trigonometric DAHA in (twisted) type A with certain rational parameters. For untwisted type A, the chapter is mainly expository. The main technical result in the twisted case is a new combinatorial classification of the irreducible representations of the DAHA which follows from the study of a map defined by Lusztig. |
| 일반주제명 | Mathematics. |
| 언어 | 영어 |
| 바로가기 | 
: 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
