Spherical Hall algebras of curves and Harder-Narasimhan stratas

الأصل · EN

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