Spherical Hall algebras of curves and Harder-Narasimhan stratas

Details Spherical Hall algebras of curves and Harder-Narasimhan stratas Spherical Hall algebras of curves and Harder-Narasimhan stratas

2010-02-04

arxiv.org/abs/1002.0987v1

Mathematics

Quantum Algebra

12 pages, Latex

Scientific paper

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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