On the Degenerate Whittaker space for some induced representations of \rm GL₄(\mathfrako₂)

2025/08/14 by Parashar, Ankita, Patel, Shiv Prakash
#20C15 #20G05 #20G25 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2508.10796

Abstract

Let \mathfrako_l be a finite principal ideal local ring of length l. The degenerate Whittaker space associated with a representation of \rm GL_2n(\mathfrako_l) is a representation of \rm GL_n(\mathfrako_l). For strongly cuspidal representations of \rm GL_2n(\mathfrako_l) the structure of degenerate Whittaker space is described by Prasad's conjecture, which has been proven for \rm GL₄(\mathfrako₂). In this paper, we describe the degenerate Whittaker space for certain induced representations of \rm GL₄(\mathfrako₂), specifically those induced from subgroups analogous to the maximal parabolic subgroups of \rm GL₄(\mathbbF_q).

Citations

• Structure of Twisted Jacquet Modules of principal series representations of Sp₄(F)
• A multiplicity one theorem for groups of type A_n over discrete valuation rings
• Regular characters of groups of type A_n over discrete valuation rings

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