From Orbital Varieties to Alternating Sign Matrices
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.
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