Notes on Sobolev spaces on compact classical groups and Stein--Sahi representations
Abstract
We discuss kernels on complact classical groups G=(n), (2n), (n) defined by the formula K(z,u)=|(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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