# On elementary version of Archimedean Langlands correspondence

Anton Gerasimov, ITEP, Russia

2012.11.07 | Christine Dilling

 Date Mon 14 Nov Time 16:15 — 17:15 Location Aud. D1

Abstract

Anton Gerasimov introduce elementary analogs of the Whittaker functions and the local Archimedean L-factors as U(n+1}-equivariant symplectic volumes of appropriate Kahler U(n+1)-manifolds. It will be demonstrated that thus defined functions have dual descriptions as matrix elements of representations of monoids GL(n+1,T), T being the tropical semifield. The existence of two representations for the elementary Whittaker functions, one as an equivariant volume and another as a matrix element
should be considered as an elementary analog of the local Archimedean Langlands duality. The elementary Whittaker functions can be also obtained from the non-Archimedean Whittaker functions over Q_p by taking a formal limit p->1. Thus the constructed elementary special functions might be considered as functions over a mysterious field Q_1.

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