On a symplectic quantum Howe duality
Representation Theory
2026-04-07 v2 Quantum Algebra
Rings and Algebras
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.
Cite
@article{arxiv.2303.04264,
title = {On a symplectic quantum Howe duality},
author = {Elijah Bodish and Daniel Tubbenhauer},
journal= {arXiv preprint arXiv:2303.04264},
year = {2026}
}
Comments
51 pages, many figures, revision, to appear in Math. Z., comments welcome