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 -