THE UNIVERSAL COVER OF SL(2,R)

Robert Shalla

Expository Article, 1996

Let SL(2,R) be the set of all 2 × 2 matrices over the real numbers with determinant 1. This expository article describes a representation theory for the universal covering group of SL(2,R) which is motivated by a localization theory due to A. Beilinson and J. Bernstein. We will explicitly describe the irreducible representations using objects familiar to the average calculus student — the complex plane, vector spaces, the algebra of 2 × 2 matrices, the derivative of a rational polynomial function — and some elementary facts about Lie group representations and algebraic D-modules.

View the entire document (16 pages)