From orbital varieties to Alternating Sign Matrices

P. Di Francesco, P. Zinn-Justin

Research output: Contribution to conferencePaperpeer-review

Abstract

We study a one-parameter family of vector-valued polynomials associated to each simple Lie algebra. When this parameter q equals -1 one recovers Joseph polynomials, whereas at q cubic root of unity one obtains ground state eigenvectors of some integrable models with boundary conditions depending on the Lie algebra; in particular, we find that the sum of its entries is related to numbers of Alternating Sign Matrices and/or Plane Partitions in various symmetry classes.

Original languageEnglish (US)
Pages95-107
Number of pages13
StatePublished - Dec 1 2006
Externally publishedYes
Event18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006 - San Diego, CA, United States
Duration: Jun 19 2006Jun 23 2006

Other

Other18th Annual International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2006
CountryUnited States
CitySan Diego, CA
Period6/19/066/23/06

Keywords

  • Algebraic combinatorics
  • Alternating Sign Matrices
  • Integrable models

ASJC Scopus subject areas

  • Algebra and Number Theory

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