| 何军华,谭友军.正交模上Clifford代数的支配权[J].数学年刊A辑,2011,32(1):11~26 |
| 正交模上Clifford代数的支配权 |
| Dominant Weights of the Clifford Algebra over an Orthogonal Module |
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| DOI： |
| 中文关键词: Clifford代数 正交模 支配权 |
| 英文关键词:Clifford algebra Orthogonal module Dominant weights |
| 基金项目:国家自然科学基金(No.10301024)资助的项目 |
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| 中文摘要: |
| 研究了正交g-模V上的Clifford代数C(V)的支配权,其中g-模C(V)是Kostant给出的旋模Spin(V)的倍数.设Δ(V)是V的非零权组成的集合.证明了Δ(V)任一正凸半的半和总是C(V)的一个支配权.反之,如果某一个半和是C(V)的重数为2(m_V(O)+dimV)/2的最高权,那么该半和一定是Δ(V)的某个正凸半的半和 |
| 英文摘要: |
| This paper deals with dominant weights of the Clifford algebra $C(V)$ over an orthogonal
$\g$-module $V$, where the $\g$-module $C(V)$ is a multiple of Kostant's spin module
${\rm Spin}(V)$. Let $\triangle(V)$ be the set of nonzero weights of $V$. The half-sum of any positive
convex half of $\triangle(V)$ is shown to be a dominant weight of $C(V)$. Conversely,
if a half-sum is a highest weight of $C(V)$ with multiplicity $2^{\frac{m_{V}(0)+\dim V}{2}}$,
then it is given by a positive convex half of $\triangle(V)$. |
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