Alladi Ramakrishnan Hall

AN INTRODUCTION TO ATLAS: BASIC BACKGROUND AND APPLICATIONS

Jonathan Fernandes

University of Maryland

Let G_R be the real points of a complex connected reductive al-
gebraic group G defined over the real numbers. The Atlas Software is a computational tool, primarily designed to compute signatures of hermitian forms on hermitian rep-
resentations of G_R. The output of the software can be used to compute a lot more than just Hermitian forms.

In this talk, we will introduce some basic terminology used by the software.

For groups of small rank, starting with SL(2, R), we will analyze it’s represen-
tations and their invariants using the software – understanding the parameters that define a representation, compute it’s infinitesimal character, character formula, composition series, the lowest K-Type, other K-types, check for unitarity etc.

It would be helpful to check out the Atlas Website at www.liegroups.org.

The ”getting started with realex” video at

www.liegroups.org/software/download/videos.html is a good place to get a quick basic introduction of the software.