The centers of spin symmetric group algebras and Catalan numbers

Details The centers of spin symmetric group algebras and Catalan numbers The centers of spin symmetric group algebras and Catalan numbers

2007-11-20

arxiv.org/abs/0711.3054v2

J. Algebr. Combin. 29 (2009), 175--193.

Mathematics

Combinatorics

18 pages, v2, added a new reference with comments in 1.3, minor changes, to appear in J. Algebraic Combinatorics

Scientific paper

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.

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