Throughout this paper, G is a finite group and Irr(G) is the set of irreducible characters of G. We are particularly interested in the values these characters take on the identity of G. If χ ∈ Irr(G), then χ(1) is the degree of χ. The set of all degrees for G is written cd(G) = {χ(1) |χ ∈ Irr(G)}. In recent years, there has been much interest in finding connections between the structure of a fi...

It is well known that the complex adjacency algebra A of an association scheme has a specific module, namely the standard module, that contains the regular module of A as a submodule. The character afforded by the standard module is called the standard character. In this paper we first define the concept of standard character for C-algebras and we say that a C-algebra has the standard character...

While we were graduate students, Marty Isaacs and I worked together on the character theory of finite groups, studying in particular the character degrees of finite p-groups. Somewhat later, my interests turned to ring theory and infinite group theory. On the other hand, Marty continued with character theory and soon became a leader in the field. Indeed, he has had a superb career as a research...

In this paper I challenge the widely held assumption that loudness is perceptual correlate of sound intensity. Drawing on psychological and neuroscientific evidence, argue best understood not as a representation any feature wave, but rather reflection salience wave representation; determined by how much attention receives. Loudness what call quantitative character, species phenomenal character ...

We present a novel input device and interface for interactively controlling the animation of graphical human character from a desktop environment. The trackers are embedded in a new physical design, which is both simple yet also provides significant benefits, and establishes a tangible interface with coordinate frames inherent to the character. A layered kinematic motion recording strategy acce...

For a finite group G, the character degree graph ∆(G) is the graph whose vertices are the primes dividing the degrees of the ordinary irreducible characters of G, with distinct primes p and q joined by an edge if pq divides some character degree of G. We determine all graphs with four vertices that occur as ∆(G) for some nonsolvable group G. Along with previously known results on character degr...