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

Yuri A. Neretin

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

表示论 2007-05-23 v1 经典分析与常微分方程

作者: Yuri A. Neretin

摘要

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.

关键词

group representations reproducing kernel hilbert space representation theory

引用

@article{arxiv.math/0411419,
  title  = {Notes on Sobolev spaces on compact classical groups and Stein--Sahi representations},
  author = {Yuri A. Neretin},
  journal= {arXiv preprint arXiv:math/0411419},
  year   = {2007}
}

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30pp

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

摘要

关键词

引用

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