Algebraic proof of explicit formulas of basic relative invariants of\n homogeneous cones

2020/11/25 by Hideto Nakashima, Nakashima, Hideto
Mathematics · #17D99 #22E25 #22F30 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic and Geometric Analysis #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2011.12588

openalex publication_date 2020/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to give another proof to a result on the image of a\nhomogeneous quadratic map which is positive with respect to a homogeneous cone,\ngiven by Graczyk and Ishi in 2014. The new proof depends on a purely algebraic\nmethod, whereas the original depends on analytic arguments. This enables us to\ngive explicit formulas of the basic relative invariants of homogeneous cones,\nobtained by the previous paper [J. Lie Theory 24 (2014), 1013--1032] without\nanalytic arguments.\n

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