2020/05/05 by Gillespie, Maria, Rhoades, Brendon · 1 citation
#05E10 (Primary) 05E05 #05E40 #20C30 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2005.02110
The classical coinvariant ring Rn is defined as the quotient of a polynomial ring in n variables by the positive-degree Sn-invariants. It has a known basis that respects the decomposition of Rn into irreducible Sn-modules, consisting of the higher specht polynomials due to Ariki, Terasoma, and Yamada. We provide an extension of the higher Specht basis to the generalized coinvariant rings Rn,k. We also give a conjectured higher Specht basis for the Garsia-Procesi modules Rμ, and provide a proof of the conjecture in the case of two-row partition shapes μ. We then combine these results to give a higher Specht basis for an infinite subfamily of the modules Rn,k,μ recently defined by Griffin, which are a common generalization of Rn,k and Rμ.