P. Di Francesco, P. Zinn-Justin
Published 2005-12-14Version 1
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.
3-enumerated alternating sign matrices
The Rotor Model with spectral parameters and enumerations of Alternating Sign Matrices
Symmetry classes of alternating sign matrices in the nineteen-vertex model
