Jucys-Murphy elements for Birman-Murakami-Wenzl algebras

Mathematics – Quantum Algebra

Scientific paper

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Proceedings of International Workshop "Supersymmetries and Quantum Symmetries", Dubna, 2009

Scientific paper

The Birman-Wenzl-Murakami algebra, considered as the quotient of the braid
group algebra, possesses the commutative set of Jucys--Murphy elements. We show
that the set of Jucys--Murphy elements is maximal commutative for the generic
Birman-Wenzl-Murakami algebra and reconstruct the representation theory of the
tower of Birman-Wenzl-Murakami algebras.

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