Lock polynomials are a (Kohnert) basis for the polynomial ring and stabilize to a basis for quasisymmetric functions containing the Schur functions. We define crystal-like operators on semistandard lock tableaux, which generate lock polynomials, and study the resulting structure. We prove these lock crystals are Demazure truncations of normal crystals at an extremal weight, analagous to Demazure crystals which are Demazure truncations of normal crystals at the highest weight. We also show that lock polynomials can be defined by divided difference operators, and we characterize when a lock polynomial is symmetric or quasisymmetric. This work is joint with Sami Assaf and was submitted as an extended abstract for FPSAC 2019.
CAGE: Philadelphia Area Combinatorics and Alg. Geometry Seminar
Thursday, November 29, 2018 - 3:00pm
George Wang
Penn