One algebra of double cosets for a general linear group over a finite field

2025/08/22 by Neretin, Yury A.
#20C05 #20G40 #20N20 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2508.16502

Abstract

Let \mathbb F_q be finite field with q elements. Let α\leqslant n be positive integers. Consider the general linear group GL(α+n, \mathbb F_q) and its subgroup H(n), which fixes the first α basis elements in \mathbb F_q^α+n. Denote A_n by the convolution algebra of H(n)-biinvariant functions on GL(α+n, \mathbb F_q) . We describe algebras A_n in terms of generators and relations and show that the family A_n admits a natural interpolation to arbitrary complex n (the field \mathbb F_q and α are fixed).

Citations

• Algebra of double cosets of a symmetric group by a smaller symmetric group
• Unitary representations of oligomorphic groups

Cited by

• Algebra of double cosets of a symmetric group by a smaller symmetric group

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