Invariant theory of $G_2$

Invariant Theory Of

Introduction. Let V denote C, and let G C SL(V) be a classical subgroup. Then Classical Invariant Theory (CIT) describes the generators and relations of the algebra of invariant polynomial functions C[raV], where m G Z and mV denotes the direct sum of m copies of V. Using the symbolic method (see [7]), one can then obtain a handle on the invariants of arbitrary representations of G. These class...

Topological Quantum Field Theory for Calabi-Yau threefolds and G_2-manifolds

On Invariant Theory

Here we develop a technique of computing the invariants of n−ary forms and systems of forms using the discriminants of corresponding multilinear forms buit of their partial derivatives, which should be cosidered as generalizations of classical discriminants and resultants for binary forms. 0 Introduction Let f(y0, y1, ..., yn) = ∑ α1≤...≤αd cα1...αdyα1 ...yαd be an n + 1−ary form of degree d, w...

Arithmetic invariant theory

Basic geometric invariant theory