Reduction mod \(p\) of cuspidal representations of \(\text{GL}_2(\mathbb F_{p^n})\) and symmetric powers.

DOI10.1016/J.JALGEBRA.2010.09.025zbMath1231.20009arXiv0909.1359OpenAlexW2042006106MaRDI QIDQ627981

Davide A. Reduzzi

Publication date: 4 March 2011

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.1359

zbMATH Keywords

general linear groupsprincipal series representationscrystalline cohomologysymmetric powerscuspidal representationscongruences for mod \(p\) modular formsmodular representations of finite groups

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Representation theory for linear algebraic groups (20G05) Modular representations and characters (20C20) Congruences for modular and (p)-adic modular forms (11F33) de Rham cohomology and algebraic geometry (14F40) Representations of finite groups of Lie type (20C33) (p)-adic cohomology, crystalline cohomology (14F30)

Related Items (3)

An explicit computation of the Hecke operator and the ghost conjecture ⋮ A local analogue of the ghost conjecture of Bergdall-Pollack ⋮ A Hecke-equivariant decomposition of spaces of Drinfeld cusp forms via representation theory, and an investigation of its subfactors

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Modular forms in characteristic \(\ell\) and special values of their \(L\)-functions
• Representations of reductive groups over finite fields
• A study of certain modular representations
• A local analysis of congruences in the \((p,p)\) case. II
• Hasse invariant and group cohomology
• Two letters on quaternions and modular forms \(\pmod p\) (with an introduction, appendix and references by R. Livné)
• Filtrations of the discrete series of \(SL_ 2(q)\) via crystalline cohomology

This page was built for publication: Reduction mod \(p\) of cuspidal representations of \(\text{GL}_2(\mathbb F_{p^n})\) and symmetric powers.