The representation theory of sl(2, ), a global approach : (preprint)
Tom H. Koornwinder · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 1980
The representation theory of SL(2,JR) is developed by the use of global (i.e.non-infinitesimal) methods.This approach is based on an explicit knowledge of the matrix elements of the principal series with respect to the K-basis.The irreducible subquotient representations of the principal series are determined, and also their Naimark equivalences and unitarizability.All irreducible K-unitary, K-finite representations of SL(2,JR) are classified, where an inversion formula for the generalised Abel transform provides an important tool.Most theorems are first proved for more general groups G, such that future applications will be possible to other semisimple groups G for which all irreducible representations are K-multiplicity free.Each section concludes with extensive bibliographic notes.