Séminaire Lotharingien de Combinatoire, 84B.53 (2020), 12 pp.
Jeremy Meza
On the Combinatorics of LLT Polynomials in Sp2n
Abstract.
LLT polynomials were originally defined as q-generating
functions for tuples of semistandard tableaux and later generalized to
arbitrary Lie type. We introduce a combinatorial definition
at q=1 for LLT polynomials of type C as a similar
generating function over tuples of symplectic tableaux. The definition
uses a correspondence between symplectic tableaux and oscillating
tableaux that is used to give a proof of a Cauchy identity
for Sp2n using Berele insertion, generalizing
the combinatorial proof of Schur-Weyl duality
for Sp2n.
Received: November 20, 2019.
Accepted: February 20, 2020.
Final version: April 30, 2020.
The following versions are available: