On some non-principal locally analytic representations induced by cuspidal Lie algebra representations

2025/05/07 by Orlik, Sascha · 1 citation
#11S37 #17B15 #17B35 #20G05 #20G25 #22E35 #22E50 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2505.04355

Abstract

Let G be a split reductive p-adic Lie group. This paper is the first in a series on the construction of locally analytic G-representations which do not lie in the principal series. Here we consider the case of the general linear group G=GL_n+1 and locally analytic representations which are induced by cuspidal modules of the Lie algebra. We prove that they are ind-admissible and satisfy the homological vanishing criterion in the definition of supercuspidality in the sense of Kohlhaase. In the case of n=1 we give a proof of their topological irreducibility for certain cuspidal modules of degree 1.

Citations

• On some non-principal locally analytic representations induced by Whittaker modules
• Cohomologie de systèmes locaux p-adiques sur les revêtements du demi-plan de Drinfeld
• On the sheaf cohomology of some p-adic period domains with coefficients in certain line bundles
• Six operations for D-cap-modules on rigid analytic spaces
• Revêtements du demi-plan de Drinfeld et correspondance de Langlands p-adique
• The Jordan-Hölder series of the locally analytic Steinberg representation
• On Jordan-Hölder series of some locally analytic representations
• Cuspidal representations of sl(n+1)
• Auslander Regularity of p-adic Distribution Algebras
• Equivariant vector bundles on Drinfeld's upper half space
• Duality for admissible locally analytic representations
• Locally analytic distributions and p-adic representation theory, with applications to GL₂
• p-adic boundary values

Cited by

• On some non-principal locally analytic representations induced by Whittaker modules

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