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a question about Can an admissible SO(n) representation contain an SO(n-1) representation with infinite multiplicity?For simplicity, just let G be GL(n) over real numbers, K=SO(n),K'=SO(n-1). Now if \pi $\pi$ is an admissible representation of G with respect to K, i.e., any irreducible K-representation occurs with finite multiplicity. Now the question I want to know that: does any irreducible K'-representation occur with finite multiplicity? |
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a question about admissible representationFor simplicity, just let G be GL(n) over real numbers, K=SO(n),K'=SO(n-1). Now if \pi is an admissible representation of G with respect to K, i.e., any irreducible K-representation occurs with finite multiplicity. Now the question I want to know that: does any irreducible K'-representation occur with finite multiplicity?
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