The centers of spin symmetric group algebras and Catalan numbers

  • Authors:

  • Jill Tysse;Weiqiang Wang

  • Affiliations:

  • Department of Mathematics, University of Virginia, Charlottesville, USA 22904;Department of Mathematics, University of Virginia, Charlottesville, USA 22904

  • Venue:
  • Journal of Algebraic Combinatorics: An International Journal
  • Year:
  • 2009

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Abstract

Generalizing the work of Farahat-Higman on symmetric groups, we describe the structures of the even centers $\mathcal{Z}_{n}$ 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 $\mathcal{Z}_{n}$ .