Branching problems of Zuckerman derived functor modules
Branching problems of Zuckerman derived functor modules
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DOI：
10.1090/conm/557/11024
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发表时间：
2011-04
期刊：
影响因子：
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通讯作者：
Toshiyuki Kobayashi
中科院分区：
文献类型：
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作者：
Toshiyuki Kobayashi
讨论了实可约群的不可约么正表示在限制于可约子群时的分支问题的最新进展。突出了$\pi$的基础$(g，K)$-模与Zuckerman的派生函子模$A_q(\lambda)$同构的情况，展示了分支律的各种丰富的特征，如无限重数、不可约限制、无重数限制、离散可分解限制等.我们还提出了一些猜想。
We discuss recent developments on branching problems of irreducible unitary representations $\pi$ of real reductive groups when restricted to reductive subgroups. Highlighting the case where the underlying $(g,K)$-modules of $\pi$ are isomorphic to Zuckerman's derived functor modules $A_q(\lambda)$, we show various and rich features of branching laws such as infinite multiplicities, irreducible restrictions, multiplicity-free restrictions, and discrete decomposable restrictions. We also formulate a number of conjectures.