Representations of SL_n over finite local rings of length two

2019/07/23 by Stasinski, Alexander
#FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1907.09878

Abstract

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

Related

• Representations of reductive groups over finite local rings of length two
• The Defining Characteristic Case of the Representations of GL_n and SL_n over Principal Ideal Local Rings
• Faithful representations of SL(2) over truncated Witt vectors
• Spectral equivalence of smooth group schemes over principal ideal local rings
• On Representations of Classical Groups over Finite Local Rings of Length Two