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arXiv · 1310.1596

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

Yury A. Neretin
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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.

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Yury A. Neretin. 2013-10-06. On multiplication of double cosets for $\GL(\infty)$ over a finite field. https://arxiv.org/abs/1310.1596

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