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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73288We 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.30ppRepresentation TheoryClassical Analysis and ODEs22E46, 243A8, 52E70, 46E35, 22E30Notes on Sobolev spaces on compact classical groups and Stein--Sahi representationstext