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Special Announcement

Computing the Hodge filtration (Unitary Dual Workshop)

Jeffrey Adams, University of Maryland

Location:  Hill 705
Date & time: Thursday, 30 January 2020 at 3:30PM - 4:30PM

The Atlas of Lie Groups and Representations implements an
algorithm to compute the signature of the invariant Hermitian form on
an irreducible representation pi of a real reductive group.  On the
other hand pi admits a canonical Hodge filtration, and Schmid and
Vilonen have conjectured there is a precise relationship between this
filtratation and the signs of the Hermitian form. I will discuss an
algorithm to compute the Hodge filtration, assuming certain expected
properties of this filtration. This algorithm, which has been
implemented in the Atlas software, is consistent with, but weaker
than Schmid and Vilonen's main conjecture.