TY - JOUR

T1 - The six-vertex model and deformations of the Weyl character formula

AU - Brubaker, Ben

AU - Schultz, Andrew

PY - 2015/6/9

Y1 - 2015/6/9

N2 - We use statistical mechanics—variants of the six-vertex model in the plane studied by means of the Yang–Baxter equation—to give new deformations of Weyl’s character formula for classical groups of Cartan type B, C, and D, and a character formula of Proctor for type BC. In each case, the corresponding Boltzmann weights are associated with the free fermion point of the six-vertex model. These deformations add to the earlier known examples in types A and C by Tokuyama and Hamel-King, respectively. A special case for classical types recovers deformations of the Weyl denominator formula due to Okada.

AB - We use statistical mechanics—variants of the six-vertex model in the plane studied by means of the Yang–Baxter equation—to give new deformations of Weyl’s character formula for classical groups of Cartan type B, C, and D, and a character formula of Proctor for type BC. In each case, the corresponding Boltzmann weights are associated with the free fermion point of the six-vertex model. These deformations add to the earlier known examples in types A and C by Tokuyama and Hamel-King, respectively. A special case for classical types recovers deformations of the Weyl denominator formula due to Okada.

KW - Statistical mechanics

KW - Weyl character formula

KW - Yang–Baxter equation

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U2 - 10.1007/s10801-015-0611-4

DO - 10.1007/s10801-015-0611-4

M3 - Article

AN - SCOPUS:84946483832

VL - 42

SP - 917

EP - 958

JO - Journal of Algebraic Combinatorics

JF - Journal of Algebraic Combinatorics

SN - 0925-9899

IS - 4

ER -