On concentration of convolutions of double cosets at   infinite-dimensional limit
  For infinite-dimensional groups $G\supset K$ the double cosets $K\setminus G/K$ 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. 
Yury A. Neretin
math.RT math.GR