Advances in Theoretical and Mathematical Physics

Volume 18 (2014)

Number 1

Idempotents for Birman-Murakami-Wenzl algebras and reflection equation

Pages: 1 – 25



A. P. Isaev (Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Moscow, Russia)

A. I. Molev (School of Mathematics and Statistics, University of Sydney, Australia)

O. V. Ogievetsky (Center of Theoretical Physics, Luminy, Marseille, France; and J.-V. Poncelet French-Russian Laboratory, UMI 2615 du CNRS, Independent University of Moscow, Russia)


A complete system of pairwise orthogonal minimal idempotents for Birman-Murakami-Wenzl algebras is obtained by a consecutive evaluation of a rational function in several variables on sequences of quantum contents of up-down tableaux. A by-product of the construction is a one-parameter family of fusion procedures for Hecke algebras. Classical limits to two different fusion procedures for Brauer algebras are described.

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