The rook partition algebra

Authors:
Cheryl Grood
Affiliations:
Department of Mathematics and Statistics, Swarthmore College, Swarthmore, PA
Venue:
Journal of Combinatorial Theory Series A
Year:
2006

Citing 3
Cited 2

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Abstract

The rook partition algebra RPk(x) is a generically semisimple algebra that arises from looking at what commutes with the action of the symmetric group Sn on U⊗k, where U is the direct sum of the natural representation and the trivial representation of Sn. We give a combinatorial description of this algebra, construct its irreducible representations, and exhibit a Murnaghan-Nakayama formula to compute certain character values.