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

Ben Brubaker, Andrew Schultz

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


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 languageEnglish (US)
Pages (from-to)917-958
Number of pages42
JournalJournal of Algebraic Combinatorics
Issue number4
StatePublished - Jun 9 2015

Bibliographical note

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

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


  • Statistical mechanics
  • Weyl character formula
  • Yang–Baxter equation


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