SCHUBERT EISENSTEIN SERIES AND POISSON SUMMATION FOR SCHUBERT VARIETIES

Schubert Eisenstein series are defined by restricting the summation in a degenerate Eisenstein series to a particular Schubert variety. In the case of GL3 over ℚ Bump and the first author proved that these Schubert Eisenstein series have meromorphic continuations in all parameters and conjectured the same is true in general. We revisit their conjecture and relate it to the program of Braverman, Kazhdan, Lafforgue, Ngô, and Sakellaridis aimed at establishing generalizations of the Poisson summation formula. We prove the Poisson summation formula for certain schemes closely related to Schubert varieties and use it to refine and establish the conjecture of Bump and the first author in many cases.

Duke Scholars

Author Jayce Robert Getz Mathematics