Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-05-14T19:33:10.576Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalized affine Springer fibres

Part of: Linear algebraic groups and related topics Lie groups Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  03 January 2012

Robert Kottwitz  and
Eva Viehmann
Robert Kottwitz
Affiliation:
Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, IL 60637, USA (kottwitz@math.uchicago.edu)
Eva Viehmann
Affiliation:
Mathematisches Institut der Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany (viehmann@math.uni-bonn.de)
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper studies two new kinds of affine Springer fibres that are adapted to the root valuation strata of Goresky–Kottwitz–MacPherson. In addition it develops various linear versions of Katz's Hodge–Newton decomposition.

Keywords

root valuation strataaffine Springer fibresHodge–Newton decomposition

MSC classification

Secondary: 11F85: $p$-adic theory, local fields 20G25: Linear algebraic groups over local fields and their integers 22E67: Loop groups and related constructions, group-theoretic treatment
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 11 , Issue 3 , July 2012 , pp. 569 - 609
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Arthur, J., The characters of discrete series as orbital integrals, Invent. Math. 32 (1976), 205–261.CrossRefGoogle Scholar
2.Borel, A., Linear algebraic groups (Benjamin, New York, 1969.)Google Scholar
3.Bruhat, F. and Tits, J., Groupes réductifs sur un corps local, I, Publ. Math. IHES 41 (1972), 5–251.CrossRefGoogle Scholar
4.Bruhat, F. and Tits, J., Groupes réductifs sur un corps local, II, Publ. Math. IHES 60 (1984), 197–376.CrossRefGoogle Scholar
5.Goresky, M., Kottwitz, R. and MacPherson, R., Codimensions of root valuation strata, Pure Appl. Math. Q. 5 (2009), 1253–1310.CrossRefGoogle Scholar
6.Harish-Chandra, , Discrete series for semisimple Lie groups, II, Acta Math. 116 (1966), 1–111.CrossRefGoogle Scholar
7.Katz, N., Slope filtration of F-crystals, Astérisque 63 (1979), 113–163.Google Scholar
8.Kazhdan, D. and Lusztig, G., Fixed point varieties on affine flag manifolds, Israel J. Math. 62 (1988), 129–168.CrossRefGoogle Scholar
9.Kottwitz, R., Isocrystals with additional structure, Compositio Math. 56 (1985), 201–220.Google Scholar
10.Kottwitz, R., On the Hodge–Newton decomposition for split groups, Int. Math. Res. Not. 26 (2003), 1433–1447.CrossRefGoogle Scholar
11.Kottwitz, R. and Rapoport, M., On the existence of F-crystals, Comment. Math. Helv. 78 (2003), 153–184.CrossRefGoogle Scholar
12.Rapoport, M. and Richartz, M., On the classification and specialization of F-isocrystals with additional structure, Compositio Math. 103 (1996), 153–181.Google Scholar
13.Sabitova, M., A simplification of root valuation data for classical groups, Alg. Representat. Theory, in press.Google Scholar
14.Viehmann, E., Connected components of closed affine Deligne–Lusztig varieties, Math. Annalen 340 (2008), 315–333.CrossRefGoogle Scholar