On a symplectic quantum Howe duality

Published 7 Mar 2023 in math.RT, math.QA, and math.RA | (2303.04264v2)

Abstract: We prove a nonsemisimple quantum version of Howe's duality with the rank 2n symplectic and the rank 2 special linear group acting on the exterior algebra of type C. We also discuss the first steps towards the symplectic analog of harmonic analysis on quantum spheres, give character formulas for various fundamental modules, and construct canonical bases of the exterior algebra.

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