G-algebras, Clifford theory, and the Green correspondence

Affine Hecke algebras, cyclotomic Hecke algebras and Clifford theory

We show that the Young tableaux theory and constructions of the irreducible representations of the Weyl groups of type A, B and D, Iwahori-Hecke algebras of types A, B, and D, the complex reflection groups G(r, p, n) and the corresponding cyclotomic Hecke algebras Hr,p,n, can be obtained, in all cases, from the affine Hecke algebra of type A. The Young tableaux theory was extended to affine Hec...

On Clifford Theory of Vertex Operator Algebras

Clifford Algebras and Graphs

I show how to associate a Clifford algebra to a graph. I describe the structure of these Clifford graph algebras and provide many examples and pictures. I describe which graphs correspond to isomorphic Clifford algebras and also discuss other related sets of graphs. This construction can be used to build models of representations of simplylaced compact Lie groups. 1 Clifford Algebras Let A be a...

Clifford algebras and spinors

This essay will present a brief outline of the theory of Clifford algebras, together with a small amount of material about quadratic forms. I follow loosely the well known book Geometric algebra by Emil Artin, but with elegant modifications that I saw originally in some lecture notes by Raoul Bott, (dating from 1962), subsequently included in [Atiyah-Bott-Shapiro:1964]. In the first section, I’...

Clifford Algebras and Spinors ∗

Expository notes on Clifford algebras and spinors with a detailed discussion of Majorana, Weyl, and Dirac spinors. The paper is meant as a review of background material, needed, in particular, in now fashionable theoretical speculations on neutrino masses. It has a more mathematical flavour than the over twenty-six-year-old Introduction to Majorana masses [1] and includes historical notes and b...