Partial isomorphisms over finite fields

Abstract

In this paper, we construct a combinatorial algebra of partial isomorphisms that gives rise to a "projective limit" of the centers of the group algebras C[GL(n,Fq)]. It allows us to prove a GL(n,Fq)-analogue of an old theorem of Farahat and Higman regarding products of conjugacy classes of permutations.

Version 2: numerous small corrections, two tables of notations to help the reader keep track of everything

References in corpus (2)

• Structure coefficients of the Hecke algebra of $(S_{2n},B_n)$
• Asymptotics of Plancherel measures for $GL(n,q)$

Cited by in corpus (2)

• Algebras of conjugacy classes in symmetric groups
• On algebras of double cosets of symmetric groups with respect to Young subgroups