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arXiv · 1002.0987

Spherical Hall algebras of curves and Harder-Narasimhan stratas

Olivier Schiffmann
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Abstract

Let X be any smooth projective curve defined over a finite field. We show that the characteristic functions of any Harder-Narasimhan strata S_a of Bun_{GL_n}X belongs to the spherical Hall algebra H_X^{sph} of X. We give a geometric analog of the above result: the intersection cohomology sheaf IC(S_a) belongs to the category of simple Eisenstein sheaves over Bun_{GL_n}X.

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Olivier Schiffmann. 2010-02-04. Spherical Hall algebras of curves and Harder-Narasimhan stratas. https://arxiv.org/abs/1002.0987

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