# Seminars & Colloquia Calendar

Special Announcement

## Unitary representations and bottom layer $$K$$-types (Unitary Dual Workshop)

#### David Vogan, MIT

Location:  Hill 705
Date & time: Wednesday, 29 January 2020 at 10:30AM - 11:30AM

Knapp about 1980 observed that unitary representations whose
infinitesimal character has nonzero imaginary part all arise by
unitary parabolic induction from strictly smaller groups. Zuckerman's
theory of "cohomological parabolic induction" leads to a similar but
slightly weaker result: unitary representations whose infinitesimal
character has "not-too-small" real part arise by cohomological induction
from strictly smaller groups.

Together these results reduce the description of unitary
representations to the case of "small" real infinitesimal character. I
will explain how to approach the (still unsolved) problem of saying
precisely what "small" means; how this is connected to the title; and
how the atlas software can help.

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