群Spin(n,1)的角和基本角
Corners and fundamental corners for the groups Spin(n,1)
摘要:
研究了群G=Spin(n,1)的不可约表示的角点和基本角点,它们不是初等的,即等价于可约非酉主列表示的子项.对于偶数n,我们得到的结果类似于[10]中对群SU(n,1)的结果。特别地,我们又得到了酉对偶$\hat{G}$的非初等部分$\hat{G}^0$与酉对偶$\hat{K}.$之间的一个双射。在n为奇数的情况下,我们得到了$\hat{G}^0$与$\hat{K}.$的一个真子集之间的一个双射
英文摘要:
We study corners and fundamental corners of the irreducible representations of the groups G=Spin(n,1) that are not elementary, i.e. that are equivalent to subquotients of reducible nonunitary principal series representations. For even n we obtain results in a way analogous to the results in [10] for the groups SU(n,1). Especially, we again get a bijection between the nonelementary part $\hat{G}^0$ of the unitary dual $\hat{G}$ and the unitary dual $\hat{K}.$ In the case of odd n we get a bijection between $\hat{G}^0$ and a tru subset of $\hat{K}.$
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