Degenerate affine Hecke algebras and centralizer construction for the symmetric groups

A. I. Molev, G. I. Olshanski

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)302-341
Number of pages40
JournalJournal of Algebra
Volume237
Issue number1
DOIs
Publication statusPublished - 1 Mar 2001
Externally publishedYes

Keywords

  • Centralizer
  • Hecke algebra
  • Symmetric group
  • Tame representation

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