The centers of spin symmetric group algebras and Catalan numbers
Abstract
Description
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.
18 pages, v2, added a new reference with comments in 1.3, minor changes, to appear in J. Algebraic Combinatorics
18 pages, v2, added a new reference with comments in 1.3, minor changes, to appear in J. Algebraic Combinatorics