正交模上Clifford代数的支配权

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.

Dominant Weights of the Clifford Algebra over an Orthogonal Module

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 $\triangle(V)$.