4 papers · 1 filter
Nonvanishing higher Specht polynomials and a construction for three row and hook shape Garsia--Procesi modules
Raymond Chou, Maria Gillespie, Mitsuki Hanada
Given a polynomial ring quotient with an action of the symmetric group induced by permuting the variables, a higher Specht basis is a collection of…
Representation Theoretic Bases for the -Springer Module
Raymond Chou, Mitsuki Hanada
We give a descent monomial basis of -Springer modules , first defined by Griffin. Our construction simultaneously generalizes the descent basis for the Garsia-Procesi…
A charge monomial basis of the Garsia-Procesi ring
Mitsuki Hanada
We construct a basis of the Garsia-Procesi ring using the catabolizability type of standard Young tableaux and the charge statistic. This basis turns out to be equal to the descent…
Polyhedral geometry of refined -Catalan numbers
Matthias Beck, Mitsuki Hanada, Max Hlavacek +3
We study a refinement of the -Catalan numbers introduced by Xin and Zhang (2022, 2023) using tools from polyhedral geometry. These refined -Catalan numbers depend on a ve…