컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0527 |
|---|---|
| 분류(Section) | Invited Talk |
| 분과(Session) | Algebra / Representation Theory / Lie Theory (SS-02) |
| 영문제목 (Title(Eng.)) |
The kernel of the multiplication map |
| 저자(Author(s)) |
Soo Teck Lee1 National University of Singapore1 |
| 초록본문(Abstract) | Let $ V_{n,p,q}$ be the $\mathrm{GL}_n= \mathrm{GL}_n( \mathbb{C}) $ module \[ V_{n,p,q}= (\overbrace{\mathbb{C} ^n\oplus \mathbb{C}^n\oplus\cdots\oplus \mathbb{C}^n}^p\oplus (\overbrace{ \mathbb{C}^{n\ast}\oplus\mathbb{C} ^{n\ast} \oplus\cdots\oplus\mathbb{C} ^{n\ast}}^q),\] and let $ \mathcal{P}(V_{n,p,q})$ be the algebra of polynomial functions on $V_{n,p,q} $. Let $\mathcal{H} $ be the space of $ \mathrm{GL}_n$ harmonic polynomials in $ \mathcal{P}(V_{n,p,q})$ and let $J= \mathcal{P}(V_{n,p,q})^{\mathrm{GL}_n }$ be the subalgebra of of $ \mathrm{GL}_n$ invariant polynomials. Consider the multiplication map \[\Phi:\mathcal{H} \otimes J\rightarrow \mathcal{P}(V_{n,p,q}).\] It is known that if $p+q\leq n$, then $\Phi$ is an isomorphism. In this talk, we will describe the kernel of $\Phi$ in the case $n\geq\min(p,q)$. This is joint work with Roger Howe. |
| 분류기호 (MSC number(s)) |
20G05, 05E15 |
| 키워드(Keyword(s)) | general linear group, harmonic polynomials, invariant polynomials |
| 강연 형태 (Language of Session (Talk)) |
English |