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arXiv · 1412.3891

Shalika germs for sl(n) and sp(2n) are motivic

Sharon Frechette·Julia Gordon·Lance Robson
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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].

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Sharon Frechette, Julia Gordon, Lance Robson. 2014-12-12. Shalika germs for sl(n) and sp(2n) are motivic. https://arxiv.org/abs/1412.3891

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