Radon transforms and the finite general linear groups

Radon Transforms and the Finite General Linear Groups

Using a class sum and a collection of related Radon transforms, we present a proof G. James’s Kernel Intersection Theorem for the complex unipotent representations of the finite general linear groups. The approach is analogous to that used by F. Scarabotti for a proof of James’s Kernel Intersection Theorem for the symmetric group. In the process, we also show that a single class sum may be used...

Radon Transforms and Finite Type Conditions

The purpose of this paper is to study averaging operators of Radon transform type. We shall formulate suitable finite type conditions and prove L-Sobolev and L → L estimates. The results will be essentially sharp for operators associated with families of curves in the plane. Let X and Y be smooth manifolds, dimX = nL, dim Y = nR, and let M be a submanifold in X×Y with conormal bundle N∗M; we de...

Multi-linear Generalised Radon Transforms 2

holds for all open sets U ⊆ Σ in a sufficiently small neighbourhood of the origin. We have already seen that (1) holds for non-trivial values of p only if the family Xπ of associated vector fields satisfies the Hörmander condition. A deeper fact is that the converse of this statement is true. This converse may be expressed in a very precise fashion which relates the range of Lebesgue exponents ...

Multi - linear Generalised Radon Transforms 1 Jonathan

On Crdaha and Finite General Linear and Unitary Groups

We show a connection between Lusztig induction operators in finite general linear and unitary groups and parabolic induction in cyclotomic rational double affine Hecke algebras. Two applications are given: an explanation of a bijection result of Broué, Malle and Michel, and some results on modular decomposition numbers of finite general groups. 2010 AMS Subject Classification: 20C33 Dedicated t...