The six-vertex model and deformations of the Weyl character formula

DOI10.1007/s10801-015-0611-4zbMath1339.82002arXiv1402.2339OpenAlexW1589845397MaRDI QIDQ902948

Andrew Schultz, Benjamin Brubaker

Publication date: 4 January 2016

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.2339

zbMATH Keywords

Yang-Baxter equationstatistical mechanicsWeyl character formulaWeyl denominator formula

Mathematics Subject Classification ID

Applications of graph theory (05C90) Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of representation theory (05E10) Representation theory for linear algebraic groups (20G05) Planar graphs; geometric and topological aspects of graph theory (05C10) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Applications of linear algebraic groups to the sciences (20G45)

Related Items (13)

Scalar products of the elliptic Felderhof model and elliptic Cauchy formula ⋮ Stochastic symplectic ice ⋮ Symmetric functions and wavefunctions of XXZ-type six-vertex models and elliptic Felderhof models by Izergin–Korepin analysis ⋮ Factorial \(Q\)-functions and Tokuyama identities for classical Lie groups ⋮ Dual wavefunction of the Felderhof model ⋮ On Hamiltonians for six-vertex models ⋮ Vertex operators, solvable lattice models and metaplectic Whittaker functions ⋮ Elliptic free-fermion model with OS boundary and elliptic Pfaffians ⋮ Dual wavefunction of the symplectic ice ⋮ Izergin-Korepin analysis on the projected wavefunctions of the generalized free-fermion model ⋮ Quantum inverse scattering method and generalizations of symplectic Schur functions and Whittaker functions ⋮ Izergin-Korepin analysis on the wavefunctions of the \(U_q(\mathrm{sl}_2)\) six-vertex model with reflecting end ⋮ A generalization of Tokuyama's formula to the Hall-Littlewood polynomials

Uses Software

• SageMath

Cites Work

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• Bijective proofs of shifted tableau and alternating sign matrix identities
• Enumerations of half-turn-symmetric alternating-sign matrices of odd order
• Odd symplectic groups
• The generating function of strict Gelfand patterns and some formulas on characters of general linear groups
• Another deformation of Weyl's denominator formula
• Symmetry classes of alternating-sign matrices under one roof
• Symplectic shifted tableaux and deformations of Weyl's denominator formula for \(\text{sp}(2n)\)
• Geometric Langlands duality and representations of algebraic groups over commutative rings
• Integrable spin chain with reflecting end
• THE CLASSICAL GROUPS. SPECTRAL ANALYSIS OF THEIR FINITE-DIMENSIONAL REPRESENTATIONS

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