On concentration of convolutions of double cosets at infinite-dimensional limit

2012/11/26 by Yury A. Neretin, Neretin, Yury A.
Mathematics · #22E66 #28C10 #43A05 #43A62 #47A48 #Analytic Number Theory Research #FOS: Mathematics #Group Theory (math.GR) #Mathematical Analysis and Transform Methods #Representation Theory (math.RT) #advanced mathematical theories #math.GR #math.RT #msc:22E66 #msc:28C10 #msc:43A05 #msc:43A62 #msc:47A48

paper · pdf · doi:10.48550/arxiv.1211.6149

14pp

arxiv created 2012/11/26 · openalex publication_date 2012/11/26 · arxiv updated 2012/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For infinite-dimensional groups G⊃ K the double cosets K∖ G/K quite often admit a structure of a semigroup; these semigroups act in K-fixed vectors of unitary representations of G. We show that such semigroups can be obtained as limits of double cosets hypergroups (or Iwahori--Hecke type algebras) on finite-dimensional (or finite) groups.

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