Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic proof of explicit formulas of basic relative invariants of
  homogeneous cones   The aim of this paper is to give another proof to a result on the image of a
homogeneous quadratic map which is positive with respect to a homogeneous cone,
given by Graczyk and Ishi in 2014. The new proof depends on a purely algebraic
method, whereas the original depends on analytic arguments. This enables us to
give explicit formulas of the basic relative invariants of homogeneous cones,
obtained by the previous paper [J. Lie Theory 24 (2014), 1013--1032] without
analytic arguments.

7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin