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An Exploration of LLT polynomials in Type C

Algebra & Discrete Mathematics

Speaker: Jeremy Meza, UC Berkeley
Location: 2112 MSB
Start time: Mon, Mar 11 2019, 12:10PM

LLT polynomials were first introduced by Lascoux, Leclerc, and Thibon in their study of plethystic substitutions of Hall-Littlewood polynomials, and they conjectured (and Leclerc and Thibon proved) that their polynomials expand on the Schur basis into polynomials in q with non-negative integer coefficients. LLT polynomials have connections to branching rules in the modular representation theory of \(S_n\), crystal bases for certain \(\mathcal{U}_q(\widehat{\mathfrak{sl}_n})\) modules, and type A Macdonald polynomials. Nevertheless, they have a simple description in terms of k-cores, k-quotients, and ribbon tableaux. I will give details on work in progress toward extending these tableau combinatorics of LLT polynomials to type C.