Notes on Sobolev spaces on compact classical groups and Stein--Sahi representations
We discuss kernels on complact classical groups \(G=\U(n)\), \(\OO(2n)\), \(\Sp(n)\) defined by the formula \(K(z,u)=|\det(1-zu^*)|^s\). We obtain the explicit Plancherel formula for these kernels and the interval of positive-definiteness. We also obtain explicit models for Sahi's 'unipote...
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| description | We discuss kernels on complact classical groups \(G=\U(n)\), \(\OO(2n)\), \(\Sp(n)\) defined by the formula \(K(z,u)=|\det(1-zu^*)|^s\). We obtain the explicit Plancherel formula for these kernels and the interval of positive-definiteness. We also obtain explicit models for Sahi's 'unipotent' representations. |
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| title | Notes on Sobolev spaces on compact classical groups and Stein--Sahi representations |
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