Relative invariants and subgeneric orbits of quivers of finite and tame type

1981 ◽  
pp. 116-124
Author(s):  
Dieter Happel
Keyword(s):  
Relative Invariants

Characterizations of symmetric cones by means of the basic relative invariants of homogeneous cones

2016 ◽  
Vol 7 (2) ◽  
Author(s):  
Hideto Nakashima
Keyword(s):  
Sufficient Conditions ◽  
Rational Functions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Symmetric Cones ◽  
The Real ◽  
Tube Domains ◽  
Homogeneous Cone ◽  
Necessary And Sufficient ◽  
Relative Invariants

AbstractIn 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].

Structures and properties of null scroll in Minkowski 3-space

2017 ◽  
Vol 14 (05) ◽  
pp. 1750066
Author(s):  
Huili Liu ◽  
Seoung Dal Jung
Keyword(s):  
Standard Equation ◽  
Structures And Properties ◽  
Relative Invariants

In this paper, we study structures and properties of Null scrolls. We define the (relative) invariants for Null scrolls by using a kind of standard equation. Using these (relative) invariants of Null scrolls, we give some new characterizations and classifications of Null scrolls and B-scrolls.

scholarly journals Invariants and relative invariants under compact Lie groups

2013 ◽  
Vol 217 (12) ◽  
pp. 2213-2220 ◽  
Author(s):  
Patrícia H. Baptistelli ◽  
Miriam Manoel
Keyword(s):  
Lie Groups ◽  
Compact Lie Groups ◽  
Relative Invariants

Projective characters and invariants of algebraic varieties

1937 ◽  
Vol 33 (2) ◽  
pp. 188-198
Author(s):  
L. Roth
Keyword(s):  
General Type ◽  
A Priori ◽  
Direct Calculation ◽  
Linear Functions ◽  
Algebraic Varieties ◽  
Arithmetic Genus ◽  
Canonical Systems ◽  
Numerical Invariants ◽  
Simple Notation ◽  
Relative Invariants

It is a familiar fact that the arithmetic genus pa and the arithmetic linear genus ω of a general surface are linear functions of its four projective characters; and we find by direct calculation that a similar property holds for the numerical invariants of a general threefold. The question thus arises, whether this result can be established a priori for any algebraic variety Vk of general type, since in that case we should have a simple means of determining its numerical invariants. It has been shown by Severi that, subject to a certain assumption, the arithmetic genus pk of Vk is a function of its projective characters, while it is known that, for k ≤ 4, pk coincides with the arithmetic genus Pa obtained by the second definition (§ 5). In the present paper we obtain, by using Severi's postulate, expressions for the arithmetic genera of a V3 and a V4 in terms of their projective characters. We obtain also the characters of their virtual canonical systems and hence derive formulae for the relative invariants Ωi. For this purpose we replace certain projective characters of Vk by others which are more easily computed and better adapted to a simple notation.

scholarly journals Relative invariants and b-functions of prehomogeneous vector spaces

1985 ◽  
Vol 98 ◽  
pp. 139-156 ◽  
Author(s):  
Yasuo Teranishi
Keyword(s):  
Vector Space ◽  
Linear Algebraic Group ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Rational Representation ◽  
Dimensional Vector Space ◽  
Finite Dimensional Vector Space ◽  
Finite Dimensional ◽  
Prehomogeneous Vector Spaces ◽  
Relative Invariants

Let G be a connected linear algebraic group, p a rational representation of G on a finite-dimensional vector space V, all defined over C.

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