On independent group characters

Hecke Characters and Formal Group Characters

Let E be an elliptic curve over Q with complex multiplication by the ring of integers of an imaginary quadratic eld. Let be the Hecke character associated to E by the theory of complex multiplication. Let be the complex conjugate character of. For a pair of integers k and j, deene the Hecke character ' = '(k; j) = k j. Let p be a prime where E has good, ordinary reduction. Let p be a xed prime ...

On the Calculation of Group Characters

In its most schematic form, the Weyl character formula can be expressed by the ratio P Q of two multinomials P ≡ a(1)+a(2) . . . a(D) and Q ≡ b(1)+b(2) . . . b(D) where D is the order of Weyl groupW (Gr) for a Lie algebra Gr of rank r. Each and every one of a(k)’s and b(k)’s is obtained by the action of a Weyl reflection, i.e. an element of W (Gr). We, instead, show that there is a way to obtai...

On an Equality Involving Group Characters

On the Computation of Group Characters

Computational methods for finding the character table of a finite group require a stock of reducible characters and techniques for decomposing these characters into irreducible characters. A method for generating reducible characters from a representation of a group is proposed. Several new techniques for computing the irreducible decompositions of a set of characters are given; these technique...

The Independent Components of Characters are 'Strokes'

What are the natural features of hand-written characters and how to arrive at them automatically? We apply independent components analysis on hand-written characters. Independent components analysis extracts the underlying statistically independent signals from a mixure of them. We expect strokes to be the independent components of handwritten characters. Our findings show that stroke-like feat...