Lift of the Trivial Representation to a Nonlinear Double Cover

Let similar to G be the nonlinear double cover of the real points of a connected, simply connected, semisimple complex group. In [16], we introduce a set of genuine small representations of similar to G with infinitesimal character., denoted similar to s. ( similar to G). In this paper, we show that similar to s./2( similar to G) is precisely the set of genuine irreducible representations arising from the KazhdanPatterson lifting of the trivial representation, when similar to G is simply laced and split.

Automated summary

This paper investigates the set of genuine small representations of the nonlinear double cover similar to G, and proves that similar to s./2 (similar to G) is precisely the set of genuine irreducible representations arising from the KazhdanPatterson lifting of the trivial representation when similar to G is simply laced and split.