OIST Representation Theory Seminar

Date

Tuesday, November 10, 2020 - 16:30 to 17:30

On Zoom

Title: Double centralizer properties for the Drinfeld double of the Taft algebras

Abstract: The Drinfeld double of the taft algebra, $$D_n$$, whose ground field contains $$n$$-th roots of unity, has a known list of 2-dimensional irreducible modules. For each of such module $$V$$, we show that there is a well-defined action of the Temperley-Lieb algebra $$TL_k$$ on the $$k$$-fold tensor product of $$V$$, and this action commutes with that of $$D_n$$. When $$V$$ is self-dual and when $$k \leq 2(n-1)$$, we further establish a isomorphism between the centralizer algebra of $$D_n$$ on $$V^{\otimes k}$$, and $$TL_k$$. Our inductive argument uses a rank function on the TL diagrams, which is compatible with the nesting function introduced by Russell-Tymoczko. This is joint work with Georgia Benkart, Rekha Biswal, Ellen Kirkman and Van Nguyen.

Zoom info can be found on the seminar webpage.

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