Journal of the Mathematical Society of Japan

Basic relative invariants of homogeneous cones and their Laplace transforms

Hideto NAKASHIMA

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Abstract

The purpose of this paper is to show that it is characteristic of symmetric cones among irreducible homogeneous cones that there exists a non-constant relatively invariant polynomial such that its Laplace transform is the reciprocal of a certain polynomial. To prove our theorem, we need the inductive structure of the basic relative invariants of a homogeneous cone. However, we actually work in a more general setting, and consider the inducing of the basic relative invariants from lower rank cones.

Article information

Source
J. Math. Soc. Japan, Volume 70, Number 1 (2018), 325-344.

Dates
First available in Project Euclid: 26 January 2018

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1516957229

Digital Object Identifier
doi:10.2969/jmsj/07017447

Mathematical Reviews number (MathSciNet)
MR3750278

Zentralblatt MATH identifier
06859854

Subjects
Primary: 44A10: Laplace transform
Secondary: 22E25: Nilpotent and solvable Lie groups 43A85: Analysis on homogeneous spaces 11S90: Prehomogeneous vector spaces

Keywords
Laplace transforms symmetric cones homogeneous cones basic relative invariants

Citation

NAKASHIMA, Hideto. Basic relative invariants of homogeneous cones and their Laplace transforms. J. Math. Soc. Japan 70 (2018), no. 1, 325--344. doi:10.2969/jmsj/07017447. https://projecteuclid.org/euclid.jmsj/1516957229


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