On a symplectic quantum Howe duality

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.

51 pages, many figures, revision, to appear in Math. Z., comments welcome

References in corpus (12)

• Webs and quantum skew Howe duality
• Canonical bases and higher representation theory
• Super $q$-Howe duality and web categories
• Cellular structures using ${\text{U}}_q$-tilting modules
• A quantum analogue of the first fundamental theorem of invariant theory
• Diagram categories for ${\text{U}}_q$-tilting modules at roots of unity
• Webs and $q$-Howe dualities in types $\mathbf{BCD}$
• Semisimplicity of Hecke and (walled) Brauer algebras
• Symmetric webs, Jones-Wenzl recursions and $q$-Howe duality
• SL2 tilting modules in the mixed case
• Quivers for SL(2) tilting modules
• Dimension formulas for some modular representations of the symplectic group in the natural characteristic