Abstract:
Elements of Lusztig's dual canonical bases are Schur-positive when evaluated on (generalized) Jacobi-Trudi matrices. This deep property was proved by Rhoades and Skandera, relying on a result of Haiman, and ultimately on the (proof of) Kazhdan-Lusztig conjecture. For a particularly tractable part of the dual canonical basis - called Temperley-Lieb immanants - we give a generalization of Littlewood-Richardson rule using shuffle tableaux. We then use our new rule to prove a special case of a Schur log-concavity conjecture by Lam-Postnikov-Pylyavskyy.
Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10. The pre-seminar and talk are online-only but will be screened in PDL C-401.
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Meeting ID: 915 4733 5974