# Degenerate affine Hecke algebras and centralizer construction for the symmetric groups

## Author

**A. I. Molev** and **G. I. Olshanski**

## Status

Research Report 2000-5

Date: 21 February 2000

## 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 increases 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 the infinite symmetric
group yield a class of natural A-modules.

## Key phrases

symmetric group. centralizer. Hecke algebra. tame representation.

## AMS Subject Classification (1991)

Primary: 20C05

Secondary: 20C32

## Content

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