Composition series for degenerate principal series of GL(n)

2015/10/18 by Dmitry Gourevitch, Gourevitch, Dmitry · 2 citations
Mathematics · #22E30 #22E50 #22F30 #46F12 #53C65 #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Metric Geometry (math.MG) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1510.05255

openalex publication_date 2015/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we consider representations of the group GL(n,F), where F is the field of real or complex numbers or, more generally, an arbitrary local field, in the space of equivariant line bundles over Grassmannians over the same field F. We study reducibility and composition series of such representations. Similar results were obtained already in [HL99,Al12,Zel80], but we give a short uniform proof in the general case, using the tools from [AGS15a]. We also indicate some applications to cosine transforms in integral geometry.

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• Period relations for Rankin-Selberg convolutions for GL(n)\timesGL(n)
• On rationality of certain Eisenstein cohomology

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