On semisimple l-modular Bernstein-blocks of a p-adic general linear group

• Verfasst von: Guiraud, David-Alexandre [VerfasserIn]
• Titel: On semisimple l-modular Bernstein-blocks of a p-adic general linear group
• Verf.angabe: David-Alexandre Guiraud
• Umfang: 25 S.
• Fussnoten: Gesehen am 16.03.2018
• Titel Quelle: Enthalten in: Journal of number theory
• Jahr Quelle: 2013
• Band/Heft Quelle: 133(2013), 10, S. 3524-3548
• ISSN Quelle: 1096-1658
• DOI: doi:10.1016/j.jnt.2013.04.012
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1571155392

Abstract

Let Gn=GLn(F), where F is a non-archimedean local field with residue characteristic p. Our starting point is the Bernstein decomposition of the representation category of Gn over an algebraically closed field of positive characteristic ℓ≠p into blocks. In level zero, we associate to each block a replacement for the Iwahori-Hecke algebra which provides a Morita equivalence as in the complex case. Additionally, we explain how this gives rise to a description of an arbitrary Gn-block in terms of simple Gm-blocks (for m⩽n), parallelling the approach of Bushnell and Kutzko in the complex setting.