Demazure crystals for flagged key polynomials

Abstract

One definition of key polynomials is as the weight generating functions of key tableaux. Assaf and Schilling introduced a crystal structure on key tableaux and related it to the Morse-Schilling crystal on reduced factorizations for per-mutations via the weak Edelman-Greene insertion. In this thesis, we consider generalizations of key tableaux and reduced factorizations depending on a flag. We extend the weak EG insertion to a bijection between our flagged objects and show that the recording tableau gives a crystal isomorphism. We prove that extending the Assaf-Schilling crystal operators to flagged key tableaux gives a Demazure crystal. As an application, we show that the weight generating functions of flagged key tableaux recover Reiner and Shimozono's definition of flagged key polynomials.

Date of Award	2024
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology
Supervisor	Eric Paul MARBERG (Supervisor)