Brauer loops and the commuting variety

Abstract

We observe that the degree of the commuting variety and other related varieties occur as coefficients in the leading eigenvector of an integrable loop model based on the Brauer algebra.

9 pages

References in corpus (6)

• Spin chains and combinatorics
• The quantum symmetric XXZ chain at Delta=-1/2, alternating sign matrices and plane partitions
• On an algebraic approach to higher dimensional statistical mechanics
• Dense loops, supersymmetry, and Goldstone phases in two dimensions
• Temperley-Lieb Stochastic Processes
• An Intersecting Loop Model as a Solvable Super Spin Chain

Cited by in corpus (3)

• Notes on Schubert, Grothendieck and Key Polynomials
• Crossover phenomena involving the dense O($n$) phase
• Completely packed O($n$) loop models and their relation with exactly solved coloring models