2019/08/14 by Drescher, C., Shepler, A. V.
#05Axx #13A50 #20F55 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1908.05259
Lewis, Reiner, and Stanton conjectured a Hilbert seriesfor a space of invariants under an action of finite general linear groups using (q,t)-binomial coefficients. This work gives an analog in positive characteristic of theorems relating various Catalan numbers to the representation theory of rational Cherednik algebras. They consider a finite general linear group as a reflection group acting on the quotient of a polynomial ring by iterated powers of the irrelevant ideal under the Frobenius map. We prove a variant of their conjecture in the local case, when the group acting fixes a reflecting hyperplane.