BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jieru Zhu (Hausdorff Institute of Mathematics) DTSTART:20201110T073000Z DTEND:20201110T083000Z DTSTAMP:20260423T021311Z UID:OISTRTS/5 DESCRIPTION:Title: Double centralizer properties for the Drinfeld double of the Taft algebras \nby Jieru Zhu (Hausdorff Institute of Mathematics) as part of OIST re presentation theory seminar\n\n\nAbstract\nThe 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 modul e $V$\, 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 com mutes 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 functio n introduced by Russell-Tymoczko. This is joint work with Georgia Benkart\ , Rekha Biswal\, Ellen Kirkman and Van Nguyen.\n LOCATION:https://researchseminars.org/talk/OISTRTS/5/ END:VEVENT END:VCALENDAR