Old and new methods for Shalika germs

Oscar Kivinen
EPFL, Lausanne, Suisse

Date(s) : 01/12/2022   iCal
11 h 00 min - 12 h 00 min

In recent work with Tsai, we give a combinatorial formula for Shalika germs of tamely ramified elements in GL_n over a non-archimedean local F. This result has many corollaries, for example the polynomiality of point-counts on local compactified Jacobians and formulas for “basic” orbital integrals of tamely ramified elements. The formula for Shalika germs comes about by combining 1) an old algorithm by Waldspurger for certain closely related germs with 2) more recent ideas from the construction of “superpolynomials” for algebraic knots using the elliptic Hall algebra. I will explain the method together with some examples and if there is time, discuss further directions such as a canonical t-deformation of the Shalika germs.


Site Sud, Luminy, Ancienne BU, Salle Séminaire2 (RdC)


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