Extremal unipotent representations for the finite Howe correspondence

• Autor: Chavez, Jesua Epequin
• Formato: artículo
• Fecha de Publicación: 2019
• Institución: Consejo Nacional de Ciencia Tecnología e Innovación
• Repositorio: CONCYTEC-Institucional
• Lenguaje: inglés
• OAI Identifier: oai:repositorio.concytec.gob.pe:20.500.12390/2852
• Enlace del recurso: https://hdl.handle.net/20.500.12390/2852; https://doi.org/10.1016/j.jalgebra.2019.05.046
• Nivel de acceso: acceso abierto
• Materia: Weyl groups; Cuspidal unipotent representations; Howe correspondence; Representation theory of finite groups; http://purl.org/pe-repo/ocde/ford#1.01.01

We study the Howe correspondence for unipotent representations of irreducible dual pairs (G, G') = (U-m (F-q), U-n(F-q)) and (G, G') = (Sp(2m)(F-q), O-2n(epsilon) (F-q)), where F-q denotes the finite field with q elements (q odd) and epsilon = +/- 1. We show how to extract extrema] (i.e. minimal and maximal) irreducible subrepresentations from the image Theta(pi') of a unipotent representation pi' of G'. (C) 2019 Elsevier Inc. All rights reserved.