Sphericity and multiplication of double cosets for infinite-dimensional classical groups

Details Sphericity and multiplication of double cosets for infinite-dimensional classical groups Sphericity and multiplication of double cosets for infinite-dimensional classical groups

2011-01-25

arxiv.org/abs/1101.4759v1

Mathematics

Representation Theory

18pages

Scientific paper

We construct spherical subgroups in infinite-dimensional classical groups $G$ (usually they are not symmetric and their finite-dimensional analogs are not spherical). We present a structure of a semigroup on double cosets $L\setminus G/L$ for various subgroups $L$ in $G$, moreover these semigroups act in spaces of $L$-fixed vectors in unitary representations of $G$. We also obtain semigroup envelops of groups $G$ generalizing constructions of operator colligations.

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