Computations of orbital integrals and Shalika germs
arXiv:2207.11296
Abstract
For a reductive group over a non-archimedean local field, with some assumptions on (residue) characteristic we give an method to compute certain orbital integrals using a method close to that of Goresky-Kottiwitz-MacPherson but in a different language. These orbital integrals allow us to compute the Shalika germs at some ``very elliptic'' elements in terms of number of rational points on some quasi-finite covers of the Hessenberg varieties of GKM, which are subvarieties of (partial) flag varieties. Such values of Shalika germs determine the Harish-Chandra local character expansions of the so-called very supercuspidal representations.
arXiv commentMost of this manuscript were written in 2014 and quite some results have been superceded. We upload this manuscript mainly for reference purpose