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Algebra & Discrete Mathematics

Speaker: Alex Chandler, UC Davis
Location: (Cancelled)
Start time: Mon, Oct 25 2021, 11:00AM

(Cancelled) This talk starts with a definition of a new combinatorial object: the doubly periodic tableau. After studying some basic combinatorial properties, we reveal the motivation for defining such objects: there is a natural action of the type A doubly affine Hecke algebra (DAHA) at roots of unity on doubly periodic tableaux. Using this action, we show that we can classify all graded X-semisimple representations of the DAHA. Analogously to the construction of Jordan and Vazirani of rectangular DAHA representations, we show that our representations can be interpreted in terms of ribbon fusion categories associated to quantum groups at roots of unity. If time permits, we will use our construction to prove a conjecture of Morton and Samuelson that the DAHA can be realized as a skein algebra of a torus with a base string modulo certain local relations.