Vertex operators, solvable lattice models and metaplectic Whittaker functions

DOI10.1007/s00220-020-03842-wzbMath1456.82097arXiv1806.07776OpenAlexW3094161755MaRDI QIDQ2216756

Valentin Buciumas, Daniel Bump, Henrik P. A. Gustafsson, Benjamin Brubaker

Publication date: 17 December 2020

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.07776

zbMATH Keywords

Kac-Moody algebrasquantum groupsYang-Baxter equationsvertex operatorHecke algebrafermionic Fock spaceDrinfeld twistsolvable lattice modelsHeisenberg spin chainsdelta ice modelgamma ice modelLam's boson-fermion correspondencemetaplectic ice modelmetaplectic symmetric functionsmetaplectic Whittaker functionsribbon symmetric functions (LLT)row transfer matrices

Mathematics Subject Classification ID

Vertex operators; vertex operator algebras and related structures (17B69) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Applications of Lie algebras and superalgebras to integrable systems (17B80) Clifford algebras, spinors (15A66) Quantum groups (quantized function algebras) and their representations (20G42) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15) Lattice dynamics; integrable lattice equations (37K60) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80) Hopf algebras and their applications (16T05) Yang-Baxter equations (16T25)

Related Items (12)

Stochastic symplectic ice ⋮ Quasi-solvable lattice models for and Demazure atoms and characters ⋮ Whittaker functions from motivic Chern classes ⋮ Colored fermionic vertex models and symmetric functions ⋮ Double Grothendieck polynomials and colored lattice models ⋮ Frozen pipes: lattice models for Grothendieck polynomials ⋮ A lattice model for super LLT polynomials ⋮ Integrable systems and crystals for edge labeled tableaux ⋮ Metaplectic representations of Hecke algebras, Weyl group actions, and associated polynomials ⋮ Free field approach to the Macdonald process ⋮ Quantum inverse scattering method and generalizations of symplectic Schur functions and Whittaker functions ⋮ Spin \(q\)-Whittaker polynomials and deformed quantum Toda

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