Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 70, Number 1 (2018), 325-344.
Basic relative invariants of homogeneous cones and their Laplace transforms
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.
J. Math. Soc. Japan, Volume 70, Number 1 (2018), 325-344.
First available in Project Euclid: 26 January 2018
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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