On an equality involving group characters

On an Equality Involving Group Characters

Equality Of Multiplicity Free Skew Characters

In this paper we show that two skew diagrams λ/μ and α/β can represent the same multiplicity free skew character [λ/μ] = [α/β] only in the the trivial cases when λ/μ and α/β are the same up to translation or rotation or if λ = α is a staircase partition λ = (l, l − 1, . . . , 2, 1) and λ/μ and α/β are conjugate of each other.

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 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...