A deformation of affine Hecke algebra and integrable stochastic particle system

2014/07/31 by Yoshihiro Takeyama · 21 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Affine transformation #Algebra over a field #Algebraic structures and combinatorial models #Deformation (meteorology) #Integrable system #Mathematics #Physics #Pure mathematics #Random Matrices and Applications #cond-mat.stat-mech #math-ph #math.MP

paper · pdf · doi:10.1088/1751-8113/47/46/465203

published in Journal of Physics A Mathematical and Theoretical 47(46), 465203 (Institute of Physics) · 18 pages, no fugure

arxiv created 2014/10/08 · openalex publication_date 2014/10/31 · arxiv updated 2015/06/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We introduce a deformation of the affine Hecke algebra of type which describes the commutation relations of the divided difference operators found by Lascoux and Schützenberger and the multiplication operators. Making use of its representation we construct an integrable stochastic particle system. It is a generalization of the q -Boson system due to Sasamoto and Wadati. We also construct eigenfunctions of its generator using the propagation operator. As a result we get the same eigenfunctions for the -Boson process obtained by Povolotsky.

Citations

• Diagonalization of an Integrable Discretization of the Repulsive Delta Bose Gas on the Circle

Cited by

• Completeness of the Bethe Ansatz for an Open \varvecq q -Boson System with Integrable Boundary Interactions
• Stochastic R matrix for Uq(An(1))

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