Bounded contractions for affine buildings
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- by Mladen Bestvina and Gordan Savin PDF
- Proc. Amer. Math. Soc. 148 (2020), 875-883 Request permission
Abstract:
We consider affine buildings with refined chamber structure. For each vertex $x$ we construct a contraction, based at $x$, that is used to prove exactness of Schneider-Stuhler resolutions of arbitrary depth.References
- Roman Bezrukavnikov, David Kazhdan, and Yakov Varshavsky, On the depth $r$ Bernstein projector, Selecta Math. (N.S.) 22 (2016), no. 4, 2271–2311. MR 3573958, DOI 10.1007/s00029-016-0278-2
- F. Bruhat and J. Tits, Groupes réductifs sur un corps local, Inst. Hautes Études Sci. Publ. Math. 41 (1972), 5–251 (French). MR 327923
- J. N. Bernstein, Le “centre” de Bernstein, Representations of reductive groups over a local field, Travaux en Cours, Hermann, Paris, 1984, pp. 1–32 (French). Edited by P. Deligne. MR 771671
- Allen Moy and Gopal Prasad, Unrefined minimal $K$-types for $p$-adic groups, Invent. Math. 116 (1994), no. 1-3, 393–408. MR 1253198, DOI 10.1007/BF01231566
- Allen Moy and Gopal Prasad, Jacquet functors and unrefined minimal $K$-types, Comment. Math. Helv. 71 (1996), no. 1, 98–121. MR 1371680, DOI 10.1007/BF02566411
- Eric Opdam and Maarten Solleveld, Resolutions of tempered representations of reductive $p$-adic groups, J. Funct. Anal. 265 (2013), no. 1, 108–134. MR 3049882, DOI 10.1016/j.jfa.2013.04.001
- Gopal Prasad and M. S. Raghunathan, Topological central extensions of semisimple groups over local fields, Ann. of Math. (2) 119 (1984), no. 1, 143–201. MR 736564, DOI 10.2307/2006967
- Peter Schneider and Ulrich Stuhler, Representation theory and sheaves on the Bruhat-Tits building, Inst. Hautes Études Sci. Publ. Math. 85 (1997), 97–191. MR 1471867
Additional Information
- Mladen Bestvina
- Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
- MR Author ID: 36095
- Email: bestvina@math.utah.edu
- Gordan Savin
- Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
- MR Author ID: 250304
- Email: savin@math.utah.edu
- Received by editor(s): April 12, 2018
- Published electronically: November 13, 2019
- Additional Notes: The first author was partially supported by NSF grant DMS-1607236.
The second author was partially supported by NSF grant DMS-1359774. - Communicated by: Alexander Braverman
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 875-883
- MSC (2010): Primary 22E50
- DOI: https://doi.org/10.1090/proc/14877
- MathSciNet review: 4052222