Notes on Sobolev spaces on compact classical groups and Stein--Sahi representations

Details Notes on Sobolev spaces on compact classical groups and Stein--Sahi representations Notes on Sobolev spaces on compact classical groups and Stein--Sahi representations

2004-11-18

arxiv.org/abs/math/0411419v1

Mathematics

Representation Theory

30pp

Scientific paper

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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