294 research outputs found
On Euler Characteristic of equivariant sheaves
Let be an algebraically closed field of characteristic and let
be another prime number. O. Gabber and F. Loeser proved that for any
algebraic torus over and any perverse -adic sheaf \calF on
the Euler characteristic \chi(\calF) is non-negative.
We conjecture that the same result holds for any perverse sheaf \calF on a
reductive group over which is equivariant with respect to the adjoint
action. We prove the conjecture when \calF is obtained by Goresky-MacPherson
extension from the set of regular semi-simple elements in . From this we
deduce that the conjecture holds for of semi-simple rank 1
Finite difference quantum Toda lattice via equivariant K-theory
We construct the action of the quantum group U_v(sl_n) by the natural
correspondences in the equivariant localized -theory of the Laumon based
Quasiflags' moduli spaces. The resulting module is the universal Verma module.
We construct geometrically the Shapovalov scalar product and the Whittaker
vectors. It follows that a certain generating function of the characters of the
global sections of the structure sheaves of the Laumon moduli spaces satisfies
a -difference analogue of the quantum Toda lattice system, reproving the
main theorem of Givental-Lee. The similar constructions are performed for the
affine Lie agebra \hat{sl}_n.Comment: Some corrections are made in Sections 2,
Twisted zastava and -Whittaker functions
In this note, we extend the results of arxiv:1111.2266 and arxiv:1203.1583 to
the non simply laced case. To this end we introduce and study the twisted
zastava spaces.Comment: 18 pages. v4: the final published versio
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