Two Dualities: Markov and Schur–Weyl
@article{Kuan2020TwoDM, title={Two Dualities: Markov and Schur–Weyl}, author={Jeffrey Kuan}, journal={arXiv: Probability}, year={2020} }
We show that quantum Schur-Weyl duality leads to Markov duality for a variety of asymmetric interacting particle systems. In particular, we consider three cases:
(1) Using a Schur-Weyl duality between a two-parameter quantum group and a two-parameter Hecke algebra from arXiv:math/0108038, we recover the Markov self-duality of multi-species ASEP previously discovered in arXiv:1605.00691 and arXiv:1606.04587.
(2) From a Schur-Weyl duality between a co-ideal subalgebra of a quantum group and a…
2 Citations
Orthogonal dualities for asymmetric particle systems *
- Mathematics
- 2021
We study a class of interacting particle systems with asymmetric interaction showing a self-duality property. The class includes the ASEP(q, θ), asymmetric exclusion process, with a repulsive…
Stochastic Baxterisation of a fused Hecke algebra
- Mathematics
- 2020
Baxterisation is a procedure which constructs solutions of the Yang–Baxter equation from algebra representations. A recent paper [Cd20b] provides Baxterisation formulas for a fused Hecke algebra. In…
References
SHOWING 1-10 OF 32 REFERENCES
Self-Duality of Markov Processes and Intertwining Functions
- MathematicsMathematical Physics, Analysis and Geometry
- 2018
We present a theorem which elucidates the connection between self-duality of Markov processes and representation theory of Lie algebras. In particular, we identify sufficient conditions such that the…
Representations of Two-Parameter Quantum Groups and Schur-Weyl Duality
- Mathematics
- 2001
We determine the finite-dimensional simple modules for two-parameter quantum groups corresponding to the general linear and special linear Lie algebras gl_n and sl_n, and give a complete reducibility…
Fused Braids and Centralisers of Tensor Representations of Uq(glN)
- MathematicsAlgebras and Representation Theory
- 2022
We present in this paper the algebra of fused permutations and its deformation the fused Hecke algebra. The first one is defined on a set of combinatorial objects that we call fused permutations, and…
From duality to determinants for q-TASEP and ASEP
- Mathematics
- 2014
We prove duality relations for two interacting particle systems: the $q$-deformed totally asymmetric simple exclusion process ($q$-TASEP) and the asymmetric simple exclusion process (ASEP).…
Quantum Algebra Symmetry of the ASEP with Second-Class Particles
- Mathematics
- 2015
We consider a two-component asymmetric simple exclusion process (ASEP) on a finite lattice with reflecting boundary conditions. For this process, which is equivalent to the ASEP with second-class…
Stochastic duality of ASEP with two particle types via symmetry of quantum groups of rank two
- Mathematics
- 2016
We study two generalizations of the asymmetric simple exclusion process (ASEP) with two types of particles, which will be called type A2 ASEP and type C2 ASEP. Particles of type 1 force particles of…
Self-Duality for the Two-Component Asymmetric Simple Exclusion Process
- Mathematics
- 2015
We study a two-component asymmetric simple exclusion process (ASEP) that is equivalent to the ASEP with second-class particles. We prove self-duality with respect to a family of duality functions…
Orthogonal Dualities of Markov Processes and Unitary Symmetries
- MathematicsSymmetry, Integrability and Geometry: Methods and Applications
- 2019
We study self-duality for interacting particle systems, where the particles move as continuous time random walkers having either exclusion interaction or inclusion interaction. We show that…
Stochastic Fusion of Interacting Particle Systems and Duality Functions
- Mathematics
- 2019
We introduce a new method, which we call stochastic fusion, which takes an exclusion process and constructs an interacting particle systems in which more than one particle may occupy a lattice site.…
Baxterisation of the fused Hecke algebra and R-matrices with gl(N)-symmetry
- MathematicsLetters in Mathematical Physics
- 2021
We give an explicit Baxterisation formula for the fused Hecke algebra and its classical limit for the algebra of fused permutations. These algebras replace the Hecke algebra and the symmetric group…