Non Spherical Principal Series Representations Of A Semisimple Lie Group

Download or read book Non-Spherical Principal Series Representations of a Semisimple Lie Group written by Alfred Magnus and published by American Mathematical Soc.. This book was released on 1979 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-spherical principal series representations of a real semisimple Lie group are studied. These are representations, induced by a one-dimensional representation of a minimal parabolic subgroup, which have a one-dimensional subspace left stable by a maximal compact subgroup of the original group G. Necessary and sufficient conditions for such a representation to be irreducible, or to be cyclic, are found, in terms of parameters determined by certain rank one subgroups of G. A sufficient condition for such a representation to be unitary is found, and the condition is shown to be necessary in the rank one case.