Two Dualities: Markov and Schur–Weyl

  title={Two Dualities: Markov and Schur–Weyl},
  author={Jeffrey Kuan},
  journal={arXiv: Probability},
  • Jeffrey Kuan
  • Published 24 June 2020
  • Mathematics
  • arXiv: Probability
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 *
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
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


Self-Duality of Markov Processes and Intertwining Functions
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
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)
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
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
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
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
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
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
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
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