Bispectral quantum Knizhnik-Zamolodchikov equations for arbitrary root systems

2009/12/18 by Michel van Meer, van Meer, Michel
Chemistry · Mathematics · Physics and Astronomy · #20C08 #Algebraic structures and combinatorial models #FOS: Mathematics #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:20C08

paper · pdf · doi:10.48550/arxiv.0912.3784

31 pages

arxiv created 2009/12/18 · openalex publication_date 2009/12/18 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The bispectral quantum Knizhnik-Zamolodchikov (BqKZ) equation corresponding to the affine Hecke algebra H of type A_N-1 is a consistent system of q-difference equations which in some sense contains two families of Cherednik's quantum affine Knizhnik-Zamolodchikov equations for meromorphic functions with values in principal series representations of H. In this paper we extend this construction of BqKZ to the case where H is the affine Hecke algebra associated to an arbitrary irreducible reduced root system. We construct explicit solutions of BqKZ and describe its correspondence to a bispectral problem involving Macdonald's q-difference operators.

Citations

• Current algebra and Wess-Zumino model in two dimensions

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