Degenerate Affine Hecke Algebras and Centralizer Construction for the Symmetric Groups

✍ Scribed by A.I Molev; G.I Olshanski

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 258 KB
• Volume: 237
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2000.8563

✦ Synopsis

In our recent papers the centralizer construction was applied to the series of Ž . classical Lie algebras to produce the quantum algebras called twisted Yangians.

Ž . Here we extend this construction to the series of the symmetric groups S n . We Ž . study the ''stable'' properties of the centralizers of S n y m in the group algebra w Ž .x ‫ރ‬ S n as n ª ϱ 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 Ž . representations of S ϱ yield a class of natural A-modules.