Clifford theory for Mackey algebras

On Clifford Theory of Vertex Operator Algebras

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...

C * - algebras and Mackey ' s theory of group representations

The subjects of C*-algebras and of unitary representations of locally compact groups are both approximately 50 years old. While it was known from the start that these subjects are related, it was noL originally appreciated just how close the relationship is, especially in the case of Mackey's theory of induced representations and of representations of group extensions. U G is a (locally compact...

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...

A theory of neural computation with Clifford algebras

The present thesis introduces Clifford Algebra as a framework for neural computation. Clifford Algebra subsumes, for example, the reals, complex numbers and quaternions. Neural computation with Clifford algebras is model–based. This principle is established by constructing Clifford algebras from quadratic spaces. Then the subspace grading inherent to any Clifford algebra is introduced, which al...