Vertex models, TASEP and Grothendieck polynomials

DOI10.1088/1751-8113/46/35/355201zbMath1278.82042arXiv1305.3030OpenAlexW3105304670MaRDI QIDQ2852211

Kazumitsu Sakai, Kohei Motegi

Publication date: 8 October 2013

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.3030

zbMATH Keywords

Yang-Baxter equationquantum inverse scattering methodwavefunctionsTASEPSchur polynomialsGrothendieck polynomialsCauchy indentityIzergin-Korepin approach

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Inverse scattering problems in quantum theory (81U40) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Groups and algebras in quantum theory and relations with integrable systems (81R12) Stochastic methods applied to problems in equilibrium statistical mechanics (82B31)

Related Items (50)

Integrable structure of multispecies zero range process ⋮ Multi-point distribution of discrete time periodic TASEP ⋮ Solving and classifying the solutions of the Yang-Baxter equation through a differential approach. Two-state systems ⋮ Type \(\widehat{\mathrm C}\) Brauer loop schemes and loop model with boundaries ⋮ Scalar products of the elliptic Felderhof model and elliptic Cauchy formula ⋮ Multipoint distribution of TASEP ⋮ Quantum Hamiltonians generated by the \(R\)-matrix of the five-vertex model ⋮ Free-fermions and skew stable Grothendieck polynomials ⋮ Symmetric functions and wavefunctions of XXZ-type six-vertex models and elliptic Felderhof models by Izergin–Korepin analysis ⋮ Dual wavefunction of the Felderhof model ⋮ Periodic TASEP with general initial conditions ⋮ Quasi-solvable lattice models for and Demazure atoms and characters ⋮ Asymptotics for the norm of Bethe eigenstates in the periodic totally asymmetric exclusion process ⋮ The 16-vertex model and its even and odd 8-vertex subcases on the square lattice ⋮ Crystal structures for canonical Grothendieck functions ⋮ Colored fermionic vertex models and symmetric functions ⋮ Refined dual Grothendieck polynomials, integrability, and the Schur measure ⋮ Double Grothendieck polynomials and colored lattice models ⋮ Frozen pipes: lattice models for Grothendieck polynomials ⋮ Grothendieck lines in 3d \(\mathcal{N} = 2\) SQCD and the quantum K-theory of the Grassmannian ⋮ Free fermions and canonical Grothendieck polynomials ⋮ Five-vertex model and Lozenge tilings of a hexagon with a dent ⋮ Integrable systems and crystals for edge labeled tableaux ⋮ Free fermions and Schur expansions of multi-Schur functions ⋮ On some quadratic algebras. I \(\frac{1}{2}\): Combinatorics of Dunkl and Gaudin elements, Schubert, Grothendieck, Fuss-Catalan, universal Tutte and reduced polynomials ⋮ Linear transformations of vertex operators of Hall-Littlewood polynomials ⋮ Colored five-vertex models and Lascoux polynomials and atoms ⋮ Vertex models for canonical Grothendieck polynomials and their duals ⋮ Combinatorial properties of symmetric polynomials from integrable vertex models in finite lattice ⋮ A class of partition functions associated with E τ,η gl3 by Izergin–Korepin analysis ⋮ Integrability approach to Fehér-Némethi-Rimányi-Guo-Sun type identities for factorial Grothendieck polynomials ⋮ Random plane partitions and corner distributions ⋮ Integrable models and \(K\)-theoretic pushforward of Grothendieck classes ⋮ The discrete Toda equation revisited: dualβ-Grothendieck polynomials, ultradiscretization, and static solitons ⋮ Duality and deformations of stable Grothendieck polynomials ⋮ Dual wavefunction of the symplectic ice ⋮ Quantum integrability and generalised quantum Schubert calculus ⋮ Grothendieck polynomials and the boson-fermion correspondence ⋮ Littlewood-Richardson coefficients for Grothendieck polynomials from integrability ⋮ On a family of symmetric rational functions ⋮ Crystal structures for symmetric Grothendieck polynomials ⋮ 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 ⋮ Colored five‐vertex models and Lascoux polynomials and atoms ⋮ Izergin-Korepin analysis on the wavefunctions of the \(U_q(\mathrm{sl}_2)\) six-vertex model with reflecting end ⋮ Dualities in quantum integrable many-body systems and integrable probabilities. I. ⋮ Riemann surface for TASEP with periodic boundaries ⋮ The partition function of the four-vertex model in inhomogeneous external field and trace statistics ⋮ Neutral-fermionic presentation of the \(K\)-theoretic \(Q\)-function ⋮ Determinant formulas for the five-vertex model

This page was built for publication: Vertex models, TASEP and Grothendieck polynomials