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 $R=\mathbb{C}[x_1,\dots ,x_n]/I$ with an action of the symmetric group induced by permuting the variables, a higher Specht basis is a collection of…