On the Eigenfunctions for the Multi-species <i>q</i>-Boson System

DOI10.1619/fesi.61.349zbMath1446.17042arXiv1606.00578OpenAlexW2963684092MaRDI QIDQ5234842

Yoshihiro Takeyama

Publication date: 4 October 2019

Published in: Funkcialaj Ekvacioj (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.00578

zbMATH Keywords

quantum groupstochastic processintegrable systemaffine Hecke algebra

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Groups and algebras in quantum theory and relations with integrable systems (81R12) Applications of Lie algebras and superalgebras to integrable systems (17B80) Orthogonal polynomials and functions associated with root systems (33C52)

Related Items (10)

A \(q\)-boson representation of Zamolodchikov-Faddeev algebra for stochastic \(R\) matrix of \(U_q(A^{(1)}_n)\) ⋮ Symmetric functions and wavefunctions of XXZ-type six-vertex models and elliptic Felderhof models by Izergin–Korepin analysis ⋮ Orthogonal polynomial duality and unitary symmetries of multi-species ASEP \((q,\boldsymbol{\theta})\) and higher-spin vertex models via \(^*\)-bialgebra structure of higher rank quantum groups ⋮ A class of partition functions associated with E τ,η gl3 by Izergin–Korepin analysis ⋮ Probability distributions of multi-species \(q\)-TAZRP and ASEP as double cosets of parabolic subgroups ⋮ Integrable models and \(K\)-theoretic pushforward of Grothendieck classes ⋮ A new generalisation of Macdonald polynomials ⋮ Quantum inverse scattering method and generalizations of symplectic Schur functions and Whittaker functions ⋮ On the Eigenfunctions for the Multi-species <i>q</i>-Boson System ⋮ Izergin-Korepin analysis on the wavefunctions of the \(U_q(\mathrm{sl}_2)\) six-vertex model with reflecting end

Cites Work

• Stochastic \(R\) matrix for \(\operatorname{U}_q(A_n^{(1)})\)
• A new generalisation of Macdonald polynomials
• On a family of symmetric rational functions
• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• On the asymmetric simple exclusion process with multiple species
• K-theoretic boson–fermion correspondence and melting crystals
• Exact results for one-dimensional totally asymmetric diffusion models
• A Multi-species ASEP $\boldsymbol{(q,\,j)}$ and $\boldsymbol{q}$-TAZRP with Stochastic Duality
• Spectral theory for the -Boson particle system
• On the Eigenfunctions for the Multi-species <i>q</i>-Boson System

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