The arithmetic and combinatorics of buildings for
Author:
Thomas R. Shemanske
Journal:
Trans. Amer. Math. Soc. 359 (2007), 34093423
MSC (2000):
Primary 20E42; Secondary 11F46, 11F60, 11F70
Published electronically:
January 30, 2007
MathSciNet review:
2299461
Fulltext PDF Free Access
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Abstract: In this paper, we investigate both arithmetic and combinatorial aspects of buildings and associated Hecke operators for with a local field. We characterize the action of the affine Weyl group in terms of a symplectic basis for an apartment, characterize the special vertices as those which are selfdual with respect to the induced inner product, and establish a onetoone correspondence between the special vertices in an apartment and the elements of the quotient . We then give a natural representation of the local Hecke algebra over acting on the special vertices of the BruhatTits building for . Finally, we give an application of the Hecke operators defined on the building by characterizing minimal walks on the building for .
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Additional Information
Thomas R. Shemanske
Affiliation:
Department of Mathematics, 6188 Kemeny Hall, Dartmouth College, Hanover, New Hampshire 03755
Email:
thomas.r.shemanske@dartmouth.edu
DOI:
http://dx.doi.org/10.1090/S0002994707042936
PII:
S 00029947(07)042936
Keywords:
BruhatTits building,
symplectic group,
Hecke operators,
representation
Received by editor(s):
January 5, 2004
Received by editor(s) in revised form:
July 12, 2005
Published electronically:
January 30, 2007
Article copyright:
© Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
