Parameters for twisted representations
نویسندگان
چکیده
One of the central problems in representation theory is understanding irreducible unitary representations. The reason is that in many applications of linear algebra (like those of representation theory to harmonic analysis) the notion of length of vectors is fundamentally important. Unitary representations are exactly those preserving a good notion of length. The paper [4] provides an algorithm for calculating the irreducible unitary representations of a real reductive Lie group. The purpose of this paper is to address a problem arising in the implementation of this algorithm. In order to explain the problem, we need to describe briefly (or at least more briefly than [4]) the nature of the algorithm. In order to minimize technicalities, we will provide in the introduction complete details only for finite-dimensional representations. For a real reductive Lie group, the theory of Harish-Chandra modules provides a complete way to deal with the complications attached to infinite-dimensional representations. To study unitary representations it is natural to study the larger class of representations with invariant Hermitian forms. Here is the underlying formalism.
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تاریخ انتشار 2015