B. Speh | Searcharxiv

arXiv2009

Discrete Components of Some Complementary Series

We show that complementary series representations of SO(n,1) contain discretely complementary series of SO(m,1) provided the continuous parameter is sufficiently close to the first point of reducibility and the representation of the compact part of the Levi is a sufficiently small fundamental representation. We prove as a consequence that cohomological representations of SO(n,1) of degree $i$ less than m/2 contain discretely, cohomogical representations of SO(m,1).

math.RT↗

arXiv2004

Construction of Some Generalised Modular Symbols

We give a criterion for the non-vanishing of some generalised modular symbols. The criterion is in terms of the non-vanishing of some classes on the compact dual of the locally symmetric manifold. As an application, we construct non-zero modular symbols on SL(2n) over an imaginary quadratic extension of $\Q$, which turn out to be ghost classes.

math.GR↗