Shalika germs for sl(n) and sp(2n) are motivic
Representation Theory
2014-12-15 v1
Abstract
We prove that Shalika germs on the Lie algebras sl(n) and sp(2n) belong to the class of so-called `motivic functions' defined by means of a first-order language of logic. We also prove, for these Lie algebras, a uniform bound of the form q^a (where q is the cardinality of the residue field) for the normalized Shalika germs. Our proof of the bound uses the theorem of Harish-Chandra that normalized Shalika germs are bounded, and a model-theoretic statement for uniform bounds of motivic functions from Appendix B to [arXiv:1208.1945].
Cite
@article{arxiv.1412.3891,
title = {Shalika germs for sl(n) and sp(2n) are motivic},
author = {Sharon Frechette and Julia Gordon and Lance Robson},
journal= {arXiv preprint arXiv:1412.3891},
year = {2014}
}
Comments
Part of this project was a collaboration started at WIN-Europe workshop, Luminy, 2013