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

2013/10/06 by Neretin, Yury A.
Mathematics · #20G40 #22B99 #22E65 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1310.1596

openalex publication_date 2013/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a group GL(∞) and its parabolic subgroup B corresponding to partition ∞=∞+m+∞. Denote by P the kernel of the natural homomorphism B→ GL(m). We show that the space of double cosets of GL(∞) 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(∞) over finite field.

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