Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From Orbital Varieties to Alternating Sign Matrices   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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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con