Orthogonal Howe duality and dynamical (split) symmetric pairs

2024/05/13 by Bodish, Elijah, Kalmykov, Artem
#17B10 (Primary) 17B37 #20F36 #32G34 #53C35 (Secondary) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2405.08126

Abstract

Inspired by Etingof--Varchenko's dynamical fusion, dynamical R-matrix, and dynamical Weyl group for Lie algebras, we introduce, for split symmetric pairs, versions of dynamical fusion, dynamical K-matrix, and dynamical Weyl group. We then turn to the study of (\mathfrakso_2n,O_m)-duality and prove that the standard Knizhnik-Zamolodchikov and dynamical operators (both differential and difference) on the \mathfrakso_2n-side are exchanged with the symmetric pair analogs, for O_m⊂ GL_m, on the O_m-side.

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