Repositorio de producción científica de la Universidad de Sevilla

The conservation relation for cuspidal representations


Advanced Search
Opened Access The conservation relation for cuspidal representations

Show item statistics
Export to
Author: Mínguez Espallargas, Alberto
Department: Universidad de Sevilla. Departamento de álgebra
Date: 2012-01
Published in: Mathematische Annalen, 352, 179-188.
Document type: Article
Abstract: Let π ∈ Cusp (U(Vn)) be a smooth cuspidal irreducible representation of a unitary group U(Vn) of dimension n over a non-Archimedean locally compact field. Let W± m the two isomorphism classes of Hermitian spaces of dimension m, and the denote by τ + ∈ Cusp U(W+m+) and τ− ∈ Cusp U(W−m−) the first non-zero theta lifts of π. In this article we prove that m+ + m− = 2n + 2, which was conjectured in [M. Harris, S. S. Kudla, J. Sweet, Theta dichotomy for unitary groups, Journal of the AMS, vol. 9, pp. 941-1004 (1996), Speculations 7.5 and 7.6]. We prove similar equalities for the other dual pairs of type I : the symplecticorthogonal dual pairs and the quaternionic dual pairs.
Cite: Mínguez Espallargas, A. (2012). The conservation relation for cuspidal representations. Mathematische Annalen, 352, 179-188.
Size: 196.6Kb
Format: PDF


DOI: 10.1007/s00208-011-0636-5

See editor´s version

This work is under a Creative Commons License: 
Attribution-NonCommercial-NoDerivatives 4.0 Internacional

This item appears in the following Collection(s)