# OIST Representation Theory Seminar

### Date

### Location

### Description

### Speaker: Jieru Zhu, Hausdorff Institute of Mathematics

### 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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