Journal of the Mathematical Society of Japan

Basic relative invariants of homogeneous cones and their Laplace transforms


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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

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

First available in Project Euclid: 26 January 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Laplace transforms symmetric cones homogeneous cones basic relative invariants


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.

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