Jucys-Murphy elements for Birman-Murakami-Wenzl algebras
A. P. Isaev, O. V. Ogievetsky
TL;DR
This paper investigates the Jucys-Murphy elements within Birman-Murakami-Wenzl algebras, establishing their maximal commutative property and reconstructing the algebra's representation theory.
Contribution
It demonstrates the maximal commutativity of Jucys-Murphy elements and reconstructs the representation theory for the tower of Birman-Wenzl-Murakami algebras.
Findings
Jucys-Murphy elements form a maximal commutative set in the algebra.
Reconstruction of the representation theory of the algebra tower.
Enhanced understanding of algebraic structure and representations.
Abstract
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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