A diagrammatic category equivalent to tilting representations of the orthogonal group is defined and its semisimplification is described, valid in characteristic not equal to two.
On a symplectic quantum Howe duality
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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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Orthogonal webs and semisimplification
A diagrammatic category equivalent to tilting representations of the orthogonal group is defined and its semisimplification is described, valid in characteristic not equal to two.