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Table of contents
Introduction
1 Comparison of constructions of supercuspidal representations: from Bushnell-Kutzko’s construction to Yu’s construction
1.1 Intertwining, compact induction and supercuspidal representations
1.2 Bushnell-Kutzko’s construction of supercuspidal representations for GLN
1.2.1 Simple strata
1.2.2 Simple characters
1.2.3 Simple types and representations
1.3 Yu’s construction of tame supercuspidal representations
1.3.1 Tamely ramied twisted Levi sequences and groups
1.3.2 Generic elements and generic characters
1.3.3 Yu data
1.3.4 Yu’s construction
1.4 Tame simple strata
1.5 Minimal elements and standard representatives
1.6 Twisted Levi sequences in GLN and generic elements associated to minimal elements
1.6.1 The group schemes of automorphisms of a free A- module of nite rank
1.6.2 Trace of endomorphisms and base change
1.6.3 Abstract twisted Levi sequences
1.6.4 Tame twisted Levi sequences
1.6.5 Generic elements associated to minimal elements .
1.7 Factorization of tame simple characters
1.7.1 Abstract factorizations of tame simple characters
1.7.2 Explicit factorizations of tame simple characters
1.8 Generic characters associated to tame simple characters
1.8.1 The characters i associated to a factorization of a tame simple character
1.8.2 The characters ^i
1.9 Extensions and main theorem of the comparison: from Bushnell- Kutzko’s construction to Yu’s construction
2 Analytic ltrations
2.1 Schemes
2.1.1 Generalities
2.1.2 Higher dilatations and congruence subgroups
2.2 Berkovich k-analytic spaces
2.2.1 k-anoid algebras
2.2.2 k-anoid spaces
2.2.3 k-analytic spaces
2.3 Bruhat-Tits buildings and Moy-Prasad ltrations
2.4 Denitions and rst properties of analytic ltrations
2.4.1 Notions of potentially Demazure objects
2.4.2 Filtrations of rational potentially Demazure k-anoid groups
2.4.3 Filtrations of Lie algebra
2.5 Filtrations associated to points in the Bruhat-Tits building .
2.5.1 Denitions and properties of Gx;r and
2.5.2 A cone
2.5.3 Comparison with Moy-Prasad ltrations in the tame case
2.5.4 Filtrations of the Lie algebra
2.5.5 Moy-Prasad isomorphism
2.5.6 Examples and pictures
APPENDIX A: About Moy-Prasad isomorphism (part of a work in progress)
APPENDIX B: On notions of rational points in the reduced Bruhat-Tits building
