From Orbital Varieties to Alternating Sign Matrices
Mathematical Physics
2007-05-23 v1 Combinatorics
math.MP
Abstract
We study a one-parameter family of vector-valued polynomials associated to each simple Lie algebra. When this parameter equals -1 one recovers Joseph polynomials, whereas at 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.
Keywords
Cite
@article{arxiv.math-ph/0512047,
title = {From Orbital Varieties to Alternating Sign Matrices},
author = {P. Di Francesco and P. Zinn-Justin},
journal= {arXiv preprint arXiv:math-ph/0512047},
year = {2007}
}