Proves nonsemisimple quantum Howe duality for Sp(2n) and SL(2) on exterior algebra of type C, with character formulas and canonical bases.
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Von Neumann algebras of Artin groups encode the number of connected components of their defining graphs except possibly for free-group-factor cases; a similar result holds for Coxeter groups absent relative hyperbolicity.
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.
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On a symplectic quantum Howe duality
Proves nonsemisimple quantum Howe duality for Sp(2n) and SL(2) on exterior algebra of type C, with character formulas and canonical bases.
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On free components of Artin and Coxeter groups
Von Neumann algebras of Artin groups encode the number of connected components of their defining graphs except possibly for free-group-factor cases; a similar result holds for Coxeter groups absent relative hyperbolicity.
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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.