Representations of SLn over finite local rings of length two

Abstract

Let Fq be a finite field of characteristic p and let W2(Fq) be the ring of Witt vectors of length two over Fq. We prove that for any integer n such that p divides n, the groups SLn(Fq[t]/t2) and SLn(W2(Fq)) have the same number of irreducible representations of dimension d, for each d.