On chiral differential operators over homogeneous spaces
Vassily Gorbounov, Fyodor Malikov, Vadim Schechtman
The notion of an algebra of chiral differential operators
(cdo for short) over a smooth
algebraic variety X has been studied by the authors previously.
We give a classification of cdo over X in the following cases:
X=G is an affine algebraic group; X=G/N or G/P where N is a unipotent
subgroup and P is a parabolic subgroup and G is simple (the extension
to the case of a semisimple G being straightforward).
The above sheaves are constructed using the BRST
(or quantum Hamiltonian) reduction of the corresponding cdo's on G.
The classification
of cdo over homogeneous spaces is exactly reflected in the BRST world:
namely the square of the corresponding BRST charge is zero at all
levels for G/N, only at the critical level for G/B and
is never zero for G/P.
V.G.: Department of Mathematics, University of Kentucky,
Lexington, KY 40506, USA;\ vgorb\@ms.uky.edu
F.M.: Department of Mathematics, University of Southern California,
Los Angeles, CA 90089, USA;\ fmalikov\@mathj.usc.edu
V.S.: IHES, 35 Route de Chartres, 91440 Bures-sur-Yvette, France;\
vadik\@ihes.fr