A CHARACTERIZATION OF SYMMETRIC CONES BY THE DEGREES OF BASIC RELATIVE INVARIANTS

被引：1

作者：

Yamasaki, Takashi ^{[1
]}

Nomura, Takaaki ^{[1
]}

机构：

[1] Kyushu Univ, Fac Math, Nishi Ku, 744 Motooka, Fukuoka 8190735, Japan

来源：

KYUSHU JOURNAL OF MATHEMATICS | 2016年 / 70卷 / 02期

关键词：

homogeneous cones; relative invariants; symmetric cones; principal minors; oriented graphs; HOMOGENEOUS CONES;

D O I：

10.2206/kyushujm.70.237

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we characterize irreducible symmetric cones among homogeneous cones Omega of rank r by the fact that the basic relative invariants for Omega and for Omega* (the dual cone of Omega) both have the degrees 1, 2,..., r, up to permutations.

引用

页码：237 / 257

页数：21

共 18 条

[1]

ASANO H, 1968, J FAC SCI U TOKYO 1, V15, P201

[2]

Bang-Jensen J., 2010, DIGRAPHS

[3]

Chartrand G., 2011, Graphs and Digraphs

[4]

Faraut J., 1994, Oxford Mathematical Monographs

[5]

Gindikin S.G., 1964, Russ. Math. Surv., V19, P1, DOI 10.1070/RM1964v019n04ABEH001153

[6] Riesz measures and Wishart laws associated to quadratic maps [J].

Graczyk, Piotr ;

Ishi, Hideyuki .

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2014, 66 (01) :317-348

[7] Positive Riesz distributions on homogeneous cones [J].

Ishi, H .

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2000, 52 (01) :161-186

[8]

Ishi H, 2001, J LIE THEORY, V11, P155

[9] Tube domain and an orbit of a complex triangular group [J].

Ishi, Hideyuki ;

Nomura, Takaaki .

MATHEMATISCHE ZEITSCHRIFT, 2008, 259 (03) :697-711

[10]

KANEYUKI S, 1974, NAGOYA MATH J, V53, P1

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