2005/12/14 by Philippe Di Francesco, P. Di Francesco, Di Francesco, P. +3
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.CO #math.MP
paper · pdf · doi:10.48550/arxiv.math-ph/0512047
arxiv created 2005/12/14 · openalex publication_date 2005/12/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.