Degenerate Affine Hecke Algebras and Centralizer Construction for the Symmetric Groups

Abstract

In our recent papers the centralizer construction was applied to the series of classical Lie algebras to produce the quantum algebras called (twisted) Yangians. Here we extend this construction to the series of the symmetric groups S(n). We study the “stable” properties of the centralizers of S(n−m) in the group algebra C[S(n)] as n→∞ with m fixed. We construct a limit centralizer algebra A and describe its algebraic structure. The algebra A turns out to be closely related with the degenerate affine Hecke algebras. We also show that the so-called tame representations of S(∞) yield a class of natural A-modules.