Alladi Ramakrishnan Hall

Classification of Discrete series by lowest K type

R. Parthasarathy

Bharatiyar University

Following the proof by Hecht and Schmid of Blattner's conjecture for K
multiplicities of representations belonging to the Discrete series
it turned out that some results which were earlier known with some
hypothesis on the Harish Chandra parameter of the
discrete class representation could be extended removing those hypothses.
For example this was so for the geometric realization problem. Occasionally
a few other results followed by first proving them for Harish Chandra
parameters which are sufficiently regular and then using Zuckerman
translation functors, wall crossing method etc.. Recently, Hongyu He raised
the question (private communication) whether the characterization of a
Discrete class representation by its lowest K-type which we proved in
collaboration with R. Hotta with some hypothesis on the Harish Chandra
parameter of the discrete class can be extendedto ALL discrete classes
excluding none, using a combination of these powerful techniques. We will
answer this question using Dirac inequality Dirac cohomology and a result
of Susana Salamanca-Riba.