Characterizations of symmetric cones by means of the basic relative invariants of homogeneous cones
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Hideto Nakashima
Abstract
In this paper, we give necessary and sufficient conditions for a homogeneous cone Ω to be symmetric in two ways. One is by using the multiplier matrix of Ω, and the other is in terms of the basic relative invariants of Ω. In the latter approach, we need to show that the real parts of certain meromorphic rational functions obtained by the basic relative invariants are always positive on the tube domains over Ω. This is a generalization of a result of Ishi and Nomura [Math. Z. 259 (2008), 604–674].
Funding source: JSPS Research Fellowships for Young Scientists
Award Identifier / Grant number: 25 · 4998
The author is grateful to Professor Takaaki Nomura for the encouragement and the comments in writing this paper. He also thanks the referee for the various comments that helped to improve this paper.
© 2016 by De Gruyter
Articles in the same Issue
- Frontmatter
- The Riesz–Herz equivalence for capacitary maximal functions on metric measure spaces
- On graded classical primary submodules
- Existence and multiplicity results for fractional p-Kirchhoff equation with sign changing nonlinearities
- Transversal hypersurfaces with (f,g,u,v,λ)-structure of a nearly trans-Sasakian manifold
- Generalized solution for a class of Hamilton–Jacobi equations
- Characterizations of symmetric cones by means of the basic relative invariants of homogeneous cones
Articles in the same Issue
- Frontmatter
- The Riesz–Herz equivalence for capacitary maximal functions on metric measure spaces
- On graded classical primary submodules
- Existence and multiplicity results for fractional p-Kirchhoff equation with sign changing nonlinearities
- Transversal hypersurfaces with (f,g,u,v,λ)-structure of a nearly trans-Sasakian manifold
- Generalized solution for a class of Hamilton–Jacobi equations
- Characterizations of symmetric cones by means of the basic relative invariants of homogeneous cones
