The orbit philosophy for Spin groups
蔡宛育教授清華大學數學系 3:30 p.m. – 5:00 p.m. 鴻經館M107Abstract：
Let G be a semisimple Lie group
with Lie algebra \g and maximal compact subgroup K. The philosophy of coadjoint
orbits suggests a way to study unitary representations of G by their close
relations to the coadjoint G-orbits on \g*. In this talk, we study a special
part of the orbit philosophy. We provide a comparison between the K-structure
of unipotent representations and regular functions of bundles on nilpotent orbits
for complex and real groups of type D. More precisely, we provide a list of
genuine unipotent representations for a Spin group; separately we compute the
K-spectra of the regular functions on certain small nilpotent orbits, and then
match them with the K-types of the genuine unipotent representations.This is
joint work with Dan Barbasch.