컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0321 |
|---|---|
| 분류(Section) | Invited Talk |
| 분과(Session) | Representation Theory (AL-2) |
| 영문제목 (Title(Eng.)) |
Explicit bases of some highest weight modules of the general linear algebra |
| 저자(Author(s)) |
Soo Teck Lee1 National University of Singapore1 |
| 초록본문(Abstract) | Let $n,p,q$ be positive integers, and let $V_{n,p,q}=(\mathbb{C}^n)^p\oplus (\mathbb{C}^{n\ast})^q$ be the $\mathrm{GL}_n$ module formed by taking the direct sum of $p$ copies of the standard module $\mathbb{C}^n$ of $q$ copies of the dual $\mathbb{C}^{n\ast}$. Then the algebra $ \mathcal{P}(V_{n,p,q})$ of polynomial functions on $V_{n,p,q} $ is a module for $\mathrm{GL}_n\times \mathfrak{gl}_{p+q}$, and it admits the decomposition \[ \mathcal{P}(V_{n,p,q})\cong \bigoplus_\lambda \rho^\lambda\otimes \sigma^\lambda\] where for each $\lambda$, $\rho^\lambda$ is an irreducible finite dimensional representation of $\mathrm{GL}_n$ and $\sigma^\lambda$ is an irreducible highest weight module of $\mathfrak{gl}_{p+q}$. In this talk, we shall construct a basis for each of the highest weight module $\sigma^\lambda$. |
| 분류기호 (MSC number(s)) |
20G05 |
| 키워드(Keyword(s)) | General linear algebra, highest weight module |
| 강연 형태 (Language of Session (Talk)) |
English |