Representations of the Rook-Brauer Algebra
نویسندگان
چکیده
We study the representation theory of the rook-Brauer algebra RBk(x), 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 RBk(x). We prove that RBk(n+1) is the centralizer of the orthogonal group On(C) on tensor space and that RBk(n+1) and On(C) are in Schur-Weyl duality. When x ∈ C is chosen so that RBk(x) is semisimple, we use its Bratteli diagram to explicitly construct a complete set of irreducible representations for RBk(x).
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