From Orbital Varieties to Alternating Sign Matrices

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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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Mathematical Physics, Combinatorics

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http://salesiana.dossiersoluciones.com/handle/123456789/106010

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math-ph/0512047
 http://arxiv.org/abs/math-ph/0512047

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arXiv