[17.11.30] Cohomology groups of equivariant vector bundles on rational homogeneous manifolds
- 홍미혜
- 조회수2310
- 2017-11-14
Cohomology groups of equivariant vector bundles on rational homogeneous manifolds
▣ 연 사 : 박경동 박사 (IBS)
▣ 일 시 : 2017년 11월 30일(목) 4:30 - 5:30
▣ 장 소 : 31351A호 (수학과 대학원 세미나실)
▣ 대 상 : 수학과 학부생 및 대학원생
▣ 다 과 : 4시 20분부터
Abstract
A rational homogeneous manifold is a homogeneous space G/P for a simple complex Lie group G and a parabolic subgroup P. This complex manifold G/P can be realized as a complex projective variety embedded into the projective space of a finite-dimensional G-module. We can construct an equivariant vector bundle on G/P from a finite-dimensional representation of P. As a key ingredient in computing the cohomology of equivariant vector bundles, I shall explain the marked Dynkin diagram with weights, and the Borel-Weil-Bott theorem which computes the sheaf cohomology of irreducible equivariant vector bundles using the Weyl group and its affine action on weights. In this talk, I will discuss the classification result about irreducible equivariant Ulrich bundles on rational homogeneous manifolds of Picard number 1. This talk is based on a joint work with Kyoung-Seog Lee.