2023/11/13 by Misha Feigin, Martin Vrabec, Feigin, Misha +1
Chemistry · Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2311.07543
openalex publication_date 2023/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Inside the double affine Hecke algebra of type GLn, which depends on two parameters q and τ, we define a subalgebra ℍ^\mathfrakgln that may be thought of as a q-analogue of the degree zero part of the corresponding rational Cherednik algebra. We prove that the algebra ℍ^\mathfrakgln is a flat τ-deformation of the crossed product of the group algebra of the symmetric group with the image of the Drinfeld-Jimbo quantum group Uq(\mathfrakgln) under the q-oscillator (Jordan-Schwinger) representation. We find all the defining relations and an explicit PBW basis for the algebra ℍ^\mathfrakgln. We describe its centre and establish a double centraliser property. As an application, we also obtain new integrable generalisations of Hamiltonians introduced by van Diejen.