戴佳玲,Doug Pickrell
DAI Jia-Ling, Doug Pickrell
摘要：
According to Kirillov’s idea, the irreducible unitary representations of a Lie
group G roughly correspond to the coadjoint orbits O. In the forward direction one applies
the methods of geometric quantization to produce a representation, and in the reverse
direction one computes a transform of the character of a representation, to obtain a coadjoint
orbit. The method of orbits in the representations of Lie groups suggests the detailed
study of coadjoint orbits of a Lie group G in the space G∗ dual to the Lie algebra G of G.
In this paper, two primary goals are achieved: one is to completely classify the smooth
coadjoint orbits of Virasoro group for nonzero central charge c; the other is to find representatives
for coadjoint orbits. These questions have been considered previously by Segal,
Kirillov, and Witten, but their results are not quite complete. To accomplish this, the
authors start by describing the coadjoint action of D-the Lie group of all orientation preserving
diffeomorphisms on the circle S1, and its central extension ˜D, then the authors will
give a complete classification of smooth coadjoint orbits. In fact, they can be parameterized
by a subspace of conjugacy classes of gPSU(1, 1). Finally, the authors will show how to find
representatives of coadjoint orbits by analyzing the vector fields stabilizing the orbits, and
describe the amazing connection between the characteristic (trace) of conjugacy classes of
gPSU(1, 1) and that of vector fields stabilizing orbits.
中图分类号: