The centers of spin symmetric group algebras and Catalan numbers
Combinatorics
2009-01-29 v2 Quantum Algebra
Representation Theory
Abstract
Generalizing the work of Farahat-Higman on symmetric groups, we describe the structures of the even centers Z_n of integral spin symmetric group superalgebras, which lead to universal algebras termed as the spin FH-algebras. A connection between the odd Jucys-Murphy elements and the Catalan numbers is developed and then used to determine the algebra generators of the spin FH-algebras and of the even centers Z_n.
Keywords
Cite
@article{arxiv.0711.3054,
title = {The centers of spin symmetric group algebras and Catalan numbers},
author = {Jill Tysse and Weiqiang Wang},
journal= {arXiv preprint arXiv:0711.3054},
year = {2009}
}
Comments
18 pages, v2, added a new reference with comments in 1.3, minor changes, to appear in J. Algebraic Combinatorics