2020/09/28 by Claire Frechette, Frechette, Claire
Mathematics · Physics and Astronomy · #16T25 (primary) 22E50 (secondary) #Black Holes and Theoretical Physics #FOS: Mathematics #Geometry and complex manifolds #Noncommutative and Quantum Gravity Theories #Number Theory (math.NT) #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2009.13669
openalex publication_date 2020/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we extend results connecting quantum groups to spherical Whittaker functions on metaplectic covers of GLr(F), for F a nonarchimedean local field. Brubaker, Buciumas, and Bump showed that for a certain metaplectic n-fold cover of GLr(F) a set of Yang-Baxter equations model the action of standard intertwiners on principal series Whittaker functions. These equations arise from a Drinfeld twist of the quantum affine Lie superalgebra U√(v)(\widehat\frakgl(n)), where v = q-1 for q the cardinality of the residue field. We extend their results to all metaplectic covers of GLr(F), providing new solutions to Yang-Baxter equations matching the scattering matrix for the associated Whittaker functions. Each cover has an associated integer invariant nQ and the resulting solutions are connected to the quantum group U√(v)(\widehat\frakgl(nQ)) and quantum superalgebra U√(v)(\widehat\frakgl(1|nQ)).