Logic and invariant theory. I. Invariant theory of projective properties

Geometric invariant theory and projective toric varieties

We define projective GIT quotients, and introduce toric varieties from this perspective. We illustrate the definitions by exploring the relationship between toric varieties and polyhedra. Geometric invariant theory (GIT) is a theory of quotients in the category of algebraic varieties. Let X be a projective variety with ample line bundle L, and G an algebraic group acting on X, along with a lift...

Combinatorial invariant theory of projective reflection groups

We introduce the class of projective reflection groups which includes all complex reflection groups. We show that several aspects involving the combinatorics and the representation theory of complex reflection groups find a natural description in this wider setting. Résumé. On introduit la classe des groupes de réflexions projectifs, ce qui généralises la notion de groupe engendré par des réfle...

The Invariant Trace Formula. I. Local Theory

Codes and invariant theory

There is a beautiful analogy between most of the notions for lattices and codes and it seems to be quite promising to develop coding theory analogues of concepts known in the theory of lattices and modular forms and vice versa. Some of these analogies are presented in this short note that intends to survey recent developments connected to my talk Hecke-Operators for codes in Luminy, on May 9, 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...