Singular invariant tempered distributions on regular prehomogeneous vector spaces

Prehomogeneous Vector Spaces and Field Extensions Ii

Free Divisors in Prehomogeneous Vector Spaces

We study linear free divisors, that is, free divisors arising as discriminants in prehomogeneous vector spaces, and in particular in quiver representation spaces. We give a characterization of the prehomogeneous vector spaces containing such linear free divisors. For reductive linear free divisors, we prove that the numbers of geometric and representation theoretic irreducible components coinci...

INVARIANT DISTRIBUTIONS ON l-SPACES

In a paper published by Ranga Rao [4] in the Annals of Mathematics, it is shown that the invariant measure carried by a nilpotent orbital can be extended to an invariant distribution on the ambient Lie algebra. This paper provides an alternative proof by a method proposed by Gordon Savin.

Generalized Character Sums Associated to Regular Prehomogeneous Vector Spaces David Kazhdan and Alexander Polishchuk

The purpose of this note is to give a short derivation of the finite field analogue of Sato’s functional equation for the zeta function associated with a prehomogeneous vector space (see [16]). We restrict ourselves to the case of a regular prehomogeneous vector space, however, we allow to twist our character sums by local systems associated to arbitrary representations of the component group o...

COMPUTATION OF CHARACTER SUMS AND APPLICATIONS TO PREHOMOGENEOUS VECTOR SPACES 1 with an appendix ” L - FUNCTIONS OF PREHOMOGENEOUS VECTOR SPACES

For an arbitrary number field K with ring of integers OK , we prove an analogue over finite rings of the form OK/p of the Fundamental Theorem on the Fourier transform of a relative invariant of prehomogeneous vector spaces, where p is a big enough prime ideal of OK and m > 1. In the appendix, F. Sato gives an application of the Theorems 1.2 and 1.5 (and Theorems A, B, C in [4]) to the functiona...