On multiplication of double cosets for $\GL(\infty)$ over a finite field

Yury A. Neretin

On multiplication of double cosets for $\GL(\infty)$ over a finite field

Representation Theory 2013-10-08 v1 Group Theory

Authors: Yury A. Neretin

Abstract

We consider a group $GL(\infty)$ and its parabolic subgroup $B$ corresponding to partition $\infty=\infty+m+\infty$ . Denote by $P$ the kernel of the natural homomorphism $B\to GL(m)$ . We show that the space of double cosets of $GL(\infty)$ by $P$ admits a natural structure of a semigroup. In fact this semigroup acts in subspaces of $P$ -fixed vectors of some unitary representations of $GL(\infty)$ over finite field.

Keywords

general linear group double cosets semigroup structure parabolic subgroup unitary representations finite fields infinite dimensional groups

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@article{arxiv.1310.1596,
  title  = {On multiplication of double cosets for $\GL(\infty)$ over a finite field},
  author = {Yury A. Neretin},
  journal= {arXiv preprint arXiv:1310.1596},
  year   = {2013}
}

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On multiplication of double cosets for $\GL(\infty)$ over a finite field

Abstract

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