Finite multiplicity theorems
Finite multiplicity theorems
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发表时间：
2011-08
影响因子：
0.7
通讯作者：
Toshiyuki Kobayashi;T. Oshima
中科院分区：
文献类型：
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作者：
Toshiyuki Kobayashi;T. Oshima
我们从闭子群H的不可约表示π中找到了半单李群G的不可约可容许表示τ在诱导表示IndHτ中的重数的上下界。作为推论，我们利用实标志簇G/P建立了HomG(π，Ind G Hτ)(诱导)和HomH(π|H，τ)(限制)的维度有限的几何判据，并利用复标志簇建立了这些重数一致有界性的判据。
We find upper and lower bounds of the multiplicities of irreducible admissible representations π of a semisimple Lie group G occurring in the induced representations IndH τ from irreducible representations τ of a closed subgroup H. As corollaries, we establish geometric criteria for finiteness of the dimension of HomG(π, Ind G H τ) (induction) and of HomH(π|H , τ) (restriction) by means of the real flag variety G/P , and criteria for uniform boundedness of these multiplicities by means of the complex flag variety.