Quantum Knizhnik-Zamolodchikov equation, totally symmetric self-complementary plane partitions, and alternating sign matrices

P. Zinn-Justin, P. Di Francesco

Research output: Contribution to journalArticle

Abstract

We present multiple-residue integral formulas for partial sums in the basis of link patterns of the polynomial solution of the level-1 Uq (sl2̂) quantum Knizhnik-Zamolodchikov equation at arbitrary values of the quantum parameter q. These formulas allow rewriting and generalizing a recent conjecture of Di Francesco connecting these sums to generating polynomials for weighted totally symmetric self-complementary plane partitions. We reduce the corresponding conjectures to a single integral identity, yet to be proved.

Original languageEnglish (US)
Pages (from-to)331-348
Number of pages18
JournalTheoretical and Mathematical Physics
Volume154
Issue number3
DOIs
StatePublished - Mar 2008
Externally publishedYes

Keywords

  • Combinatorics
  • Loop model
  • Quantum integrability

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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