Geodesic
Refined Cauchy/Littlewood identities and six-vertex model partition functions. II: proofs and new conjectures
Journal of Algebraic Combinatorics, Tome 42 (2015) no. 2, pp. 555-603.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We prove two identities of Hall-Littlewood polynomials, which appeared recently in D. Betea and M. Wheeler ["Refined Cauchy and Littlewood identities, plane partitions, and symmetry classes of alternating sign matrices", Preprint, arXiv:1402.0229]. We also conjecture, and in some cases prove, new identities which relate infinite sums of symmetric polynomials and partition functions associated with symmetry classes of alternating sign matrices. These identities generalize those already found in Betea and Wheeler [loc. cit.], via the introduction of additional parameters. The left-hand side of each of our identities is a simple refinement of a relevant Cauchy or Littlewood identity. The right-hand side of each identity is (one of the two factors present in) the partition function of the six-vertex model on a relevant domain.
Classification : 05E05, 33D52, 82B20
Keywords: Cauchy identity, Littlewood identity, symmetric functions, alternating sign matrices, six-vertex model 
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     author = {Betea, D. and Wheeler, M. and Zinn-Justin, P.},
     title = {Refined {Cauchy/Littlewood} identities and six-vertex model partition functions. {II:} proofs and new conjectures},
     journal = {Journal of Algebraic Combinatorics},
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Betea, D.; Wheeler, M.; Zinn-Justin, P. Refined Cauchy/Littlewood identities and six-vertex model partition functions. II: proofs and new conjectures. Journal of Algebraic Combinatorics, Tome 42 (2015) no. 2, pp. 555-603. http://geodesic.mathdoc.fr/item/JAC_2015__42_2_a3/