Alladi Ramakrishnan Hall

Nilpotent orbits in flag varieties and associated varieties

Gautam Gopal Krishnan

Cornell

Nilpotent orbits in flag varieties and associated varieties
Abstract: Starting with a complex reductive Lie group, the Schubert (or
Bruhat) decomposition provides a starting point to study the geometry and
topology of flag varieties. Generalising this to multiple flag varieties
leads to questions about group actions on homogeneous spaces. We will
discuss this generalisation of flag varieties and talk about the nilpotent
orbits that show up naturally. Nilpotent orbits of a similar flavour are an
important tool to understand certain irreducible representations of real
reductive Lie groups. In particular, we will talk about the associated
varieties of discrete series representations as studied by David Vogan which
builds on a long series of work starting from Harish-Chandra.