Extending the Steinberg representation

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...

The Steinberg Wiring Problem

Extending the classical view of representation.

Representation has always been a central part of models in cognitive science, but this idea has come under attack. Researchers advocating the alternative approaches of perceptual symbol systems, situated action, embodied cognition, and dynamical systems have argued against central assumptions of the classical representational approach to mind. We review the core assumptions of the representatio...

Bessel models and L-functions for the Steinberg representation of GSp4

We obtain explicit formulas for the test vector in the Bessel model and derive the criteria for existence and uniqueness for Bessel models for the unramified, quadratic twists of the Steinberg representation π of GSp4(F ), where F is a non-archimedean local field of characteristic zero. We also give precise criteria for the Iwahori spherical vector in π to be a test vector. We apply the formula...

Se p 20 09 Steinberg representation of GSp 4 : Bessel models and integral representation of L - functions

Abstract. We obtain explicit formulas for the test vector in the Bessel model and derive the criteria for existence and uniqueness for Bessel models for the unramified, quadratic twists of the Steinberg representation π of GSp 4 (F ), where F is a non-archimedean local field of characteristic zero. We also give precise criteria for the Iwahori spherical vector in π to be a test vector. We apply...