The Drinfeld double of the Taft algebra, Dn, whose ground field contains nth 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 TLk on the k-fold tensor product of V, and this action commutes with that of Dn. When V is self-dual and when k ≤ 2(n−1), we further establish a isomorphism between the centralizer algebra of Dn on V⊗k, and TLk. 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.
This video was produced by the Okinawa Institute of Science and Technology, as part of their OIST Representation Theory Seminar series.
