Representations of the Rook-Brauer Algebra

By Tom Halverson, Elise delMas. 2012

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We study the representation theory of the rook-Brauer algebra , which has a of Brauer diagrams that allow for the possibility of missing edges. The Brauer, Temperley–Lieb, Motzkin, rook monoid, and symmetric group algebras are subalgebras of . We prove that is the centralizer of the orthogonal group on tensor space and that and are in Schur–Weyl duality. When x ∈ ℂ is chosen so that is semisimple, we use its Bratteli diagram to explicitly construct a complete set of irreducible representations for .

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

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