Airy sheaves for reductive groups

Γ-sheaves on Reductive Groups

Let G be a reductive group over a finite field F = Fq. Fix a non-trivial additive character ψ : F → Q × l . In [3] we introduced certain γ-functions γG,ρ,ψ on the set Irr(G) of irreducible representations of the finite group G = G(F ). As usual every function γG,ρ,ψ on Irr(G) gives rise to an AdG-equivariant function ΦG,ρ,ψ on G. The purpose of this paper is to construct an irreducible perverse...

A Gauss-Bonnet theorem for constructible sheaves on reductive groups

In this paper, we prove an analog of the Gauss-Bonnet formula for constructible sheaves on reductive groups. As a corollary from this formula we get that if a perverse sheaf on a reductive group is equivariant under the adjoint action, then its Euler characteristic is nonnegative. In the sequel by a constructible complex we will always mean a bounded complex of sheaves of C-vector spaces whose ...

Monodromy of Airy and Kloosterman Sheaves

The simplicity of this equation makes these hyperelliptic curves particularly well suited for explicit computer calculations requiring higher genus curves. On the other hand, the special form of the equation raises the question of how generic or random, if at all, these curves are. For instance, all of these curves have 2-rank 0. The question of genericity can be restated more precisely as the ...

Airy Functions for Compact Lie Groups

The classical Airy function has been generalised by Kontsevich to a function of a matrix argument, which is an integral over the space of (skew) hermitian matrices of a unitary-invariant exponential kernel. In this paper, the Kontsevich integral is generalised to integrals over the Lie algebra of an arbitrary connected compact Lie group, using exponential kernels invariant under the group. The ...

Reductive Groups