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

Ben Brubaker; Andrew Schultz

doi:10.1007/s10801-015-0611-4

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

Ben Brubaker, Andrew Schultz

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	917-958
Number of pages	42
Journal	Journal of Algebraic Combinatorics
Volume	42
Issue number	4
DOIs	https://doi.org/10.1007/s10801-015-0611-4
State	Published - Jun 9 2015
Externally published	Yes

Bibliographical note

Funding Information:
This work was partially supported by NSF Grant DMS-1258675.

Publisher Copyright:
© 2015, Springer Science+Business Media New York.

Keywords

Statistical mechanics
Weyl character formula
Yang–Baxter equation

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10.1007/s10801-015-0611-4

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AU - Schultz, Andrew

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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.

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KW - Weyl character formula

KW - Yang–Baxter equation

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

Abstract

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