Orthogonal Polynomial Stochastic Duality Functions for Multi-Species SEP$(2j)$ and Multi-Species IRW

Abstract

We obtain orthogonal polynomial self-duality functions for multi-species version of the symmetric exclusion process (SEP$(2j)$) and the independent random walker process (IRW) on a finite undirected graph. In each process, we have $n>1$ species of particles. In addition, we allow up to $2j$ particles to occupy each site in the multi-species SEP$(2j)$. The duality functions for the multi-species SEP$(2j)$ and the multi-species IRW come from unitary intertwiners between different $\ast$-representations of the special linear Lie algebra ${\mathfrak{sl}}_{n+1}$ and the Heisenberg Lie algebra ${\mathfrak{h}}_n$, respectively. The analysis leads to multivariate Krawtchouk polynomials as orthogonal duality functions for the multi-species SEP$(2j)$ and homogeneous products of Charlier polynomials as orthogonal duality functions for the multi-species IRW.

References in corpus (8)

• Duality and hidden symmetries in interacting particle systems
• A Lie theoretic interpretation of multivariate hypergeometric polynomials
• Factorized duality, stationary product measures and generating functions
• A Multi-species ASEP(q,j) and q-TAZRP with Stochastic Duality
• On the spectral gap of the Kac walk and other binary collision processes
• Orthogonal Dualities of Markov Processes and Unitary Symmetries
• Stochastic Fusion of Interacting Particle Systems and Duality Functions
• Higher order hydrodynamics and equilibrium fluctuations of interacting particle systems

Cited by in corpus (1)

• A Generalized Dynamic Asymmetric Exclusion Process: Orthogonal Dualities and Degenerations