Opened Access Représentations banales de GLm(D)

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Author: Mínguez Espallargas, Alberto
Department: Universidad de Sevilla. Departamento de álgebra
Date: 2013
Published in: Compositio Mathematica, 149, 679-704.
Document type: Article
Abstract: Let F be a non-Archimedean locally compact field of residue characteristic p, let D be a finite dimensional central division F-algebra and let R be an algebraically closed field of characteristic different from p. We define banal irreducible R-representations of the group G = GLm(D). This notion involves a condition on the cuspidal support of the representation depending on the characteristic of R. When this characteristic is banal with respect to G, in particular when R is the field of complex numbers, any irreducible R-representation of G is banal. In this article, we give a classification of all banal irreducible R-representations of G in terms of certain multisegments, called banal. When R is the field of complex numbers, our method provides a new proof, entirely local, of Tadi´c’s classification of irreducible complex smooth representations of G.
Cite: Mínguez Espallargas, A. (2013). Représentations banales de GLm(D). Compositio Mathematica, 149, 679-704.
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DOI: 10.1112/S0010437X12000590

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