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

The paper is available in the following forms:

TeX dvi format:: 2000-5.dvi.gz (57kB) or 2000-5.dvi (149kB)
PostScript:: 2000-5.ps.gz (145kB) or 2000-5.ps (392kB)

To minimize network load, please choose the smaller gzipped .gz form if and only if your browser client supports it.

Sydney Mathematics and Statistics