8 papers
Degenerations and contractions of algebras and forms
Harold N. Ward
This note intertwines the concepts of degeneration and contraction of algebras and quadratic forms defined on a vector space V . The general linear group GL(V ) acts regularly on t…
A Normal Graph Algebra
Harold N. Ward
We define a normal graph algebra modeled on algebras used in genetics. Although the algebra does not always determine its graph, it often highlights special features. After develop…
Linear degenerations of algebras and certain representations of the general linear group
Christakis A. Pallikaros, Harold N. Ward
Let , where is a field with , be the space of structure vectors of algebras having the -dimensional $\mathbb{F}…
Thirty-six Officers and their Code
Harold N. Ward
This note presents a short proof of Euler's 36 officer conjecture. This implies that there is no affine plane of order , but we also give a direct proof.
Matrices for the Weil representation
Harold N. Ward
These notes contain a revisit to the matrix construction of the Weil representation by the author in the Journal of Algebra in 1972.
Groups from class 2 algebras and the Weil character
Christakis A. Pallikaros, Harold N. Ward
We investigate the behaviour of the Weil character of the symplectic group on restriction to subgroups arising from commutative nilpotent algebras of class 2. We give explicit desc…