Quantum walled Brauer algebra: commuting families, Baxterization, and representations

Abstract

For the quantum walled Brauer algebra, we construct its Specht modules and (for generic parameters of the algebra) seminormal modules. The latter construction yields the spectrum of a commuting family of Jucys--Murphy elements. We also propose a Baxterization prescription; it involves representing the quantum walled Brauer algebra in terms of morphisms in a braided monoidal category and introducing parameters into these morphisms, which allows constructing a "universal transfer matrix" that generates commuting elements of the algebra.

V3: 54pp., minor changes and corrections (mainly suggested by the referee); references updated

References in corpus (3)

• Algebraic Bethe ansatz for the quantum group invariant open XXZ chain at roots of unity
• Commuting Families in Temperley-Lieb Algebras
• Some new applications of the Stanley-Macdonald Pieri Rules

Cited by in corpus (2)

• Supersymmetric polynomials and the center of the walled Brauer algebra
• Bimodule structure of the mixed tensor product over $U_{q}s\ell (2|1)$ and quantum walled Brauer algebra