Character sums and intersection cohomology complexes associated to the space of square matrices
type: Item
instance of: scholarly article
title: Character sums and intersection cohomology complexes associated to the space of square matrices
zbMATH Open document ID: 0921.11066
DOI: 10.1016/S0019-3577(97)81816-2
author: Akihiko Gyoja
published in: Indagationes Mathematicae. New Series
publication date: 1998-05-13T00:00:00Z
review text: The author studies Fourier transforms of relatively invariant functions on the square matrix spaces and Hermitian matrix spaces over the finite field \(\mathbb{F}_q\), which are typical prehomogeneous vector spaces over a finite field. In the general setting, the formula of Fourier transform of a relatively invariant function on a prehomogeneous vector space was already obtained by the author provided that the characteristic of \(\mathbb{F}_q\) is sufficiently large and that we consider only the open orbit of the prehomogeneous vector space. One purpose of this paper is to exclude the constraint in these special examples and give an explicit formula of the Fourier transform. Though in this paper we only consider two examples, this is the first step to the study of prehomogeneous vector spaces using intersection cohomology theory.
Mathematics Subject Classification ID: 11T24
Mathematics Subject Classification ID: 14F43
Mathematics Subject Classification ID: 14M17
zbMATH DE Number: 1136777
zbMATH Keywords: Gauss sum
zbMATH Keywords: character sum
zbMATH Keywords: Fourier transforms of relatively invariant functions
zbMATH Keywords: square matrix spaces
zbMATH Keywords: Hermitian matrix spaces
zbMATH Keywords: finite field
zbMATH Keywords: prehomogeneous vector spaces
zbMATH Keywords: intersection cohomology theory
reviewed by: Masakazu Muro
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1136777