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

P. Zinn-Justin; P. Di Francesco

doi:10.1007/s11232-008-0031-x

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

Research output: Contribution to journal › Article › peer-review

Abstract

We present multiple-residue integral formulas for partial sums in the basis of link patterns of the polynomial solution of the level-1 U_q (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 language	English (US)
Pages (from-to)	331-348
Number of pages	18
Journal	Theoretical and Mathematical Physics
Volume	154
Issue number	3
DOIs	https://doi.org/10.1007/s11232-008-0031-x
State	Published - Mar 2008
Externally published	Yes

Keywords

Combinatorics
Loop model
Quantum integrability

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

Online availability

10.1007/s11232-008-0031-x

Library availability

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

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 (sl{\^2}) 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.",

keywords = "Combinatorics, Loop model, Quantum integrability",

author = "P. Zinn-Justin and {Di Francesco}, P.",

note = "Funding Information: This work was supported by the European Marie Curie Research Training Networks “ENIGMA” (Grant No. MRT-CT-2004-5652) and “ENRAGE” (Grant No. MRTN-CT-2004-005616), the ESF program “MIS-GAM,” and the ANR program “GIMP” (Grant No. ANR-05-BLAN-0029-01).",

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N2 - 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.

AB - 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.

KW - Combinatorics

KW - Loop model

KW - Quantum integrability

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

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