Daniel Steinberg, 1922–2015

The Steinberg Representation

Introduction. Group representations occupy a sort of middle ground between abstract groups and transformation groups, i.e., groups acting in concrete ways as permutations of sets, homeomorphisms of topological spaces, diffeomorphisms of manifolds, etc. The requirement that the elements of a group act as linear operators on a vector space limits somewhat the complexity of the action without sacr...

Steinberg groups as amalgams

For any root system and any commutative ring, we give a relatively simple presentation of a group related to its Steinberg group St. This includes the case of infinite root systems used in Kac–Moody theory, for which the Steinberg group was defined by Tits and Morita–Rehmann. In most cases, our group equals St, giving a presentation with many advantages over the usual presentation of St. This e...

The Steinberg Wiring Problem

Steinberg Modules and Donkin Pairs

We prove that in characteristic p > 0 a module with good filtration for a group of type E6 restricts to a module with good filtration for a group of type F4. Thus we confirm a conjecture of Brundan for one more case. Our method relies on the canonical Frobenius splittings of Mathieu. Next we settle the remaining cases, in characteristic not 2, with a computer-aided variation on the old method o...

Daniel Goldenholz

A novel approach to temporal pattern recognition was recently introduced in the literature, called liquid computing. The model used was very complex, thus the present study uses a simplified version that is easier to understand. By exploring properties of the system with the simple setup, a better unders tanding of the complex version can be reached. A liquid computer needs a liquid memory and ...