Research
My research interests are in the general area of Representation Theory. More precisely, Weight modules over finite- and infinite-dimensional Lie algebras and Lie superalgebras; Harish-Chandra modules; Geometry of infinite-dimensional flag manifolds, homogeneous spaces and D-modules; Borel-Weil-Bott theory of infinite-dimensional homogeneous spaces; Super geometry.
For more details, see some of my papers:
- Ind-varieties of generalized flags as homogeneous spaces for classical ind--groups, preprint, 2001, 14 pp.
(with I. Penkov) [PDF 249KB]
- A Bott-Borel-Weil theory for direct limits of algebraic groups, American Journal of Math., to appear.
(with I. Penkov and J. A. Wolf) [PDF 419KB]
- On the structure of weight modules, Transactions AMS 352 (2000), 2857-2869.
(with O. Mathieu and I. Penkov) [PDF 210KB]
- Weight modules of direct limit Lie algebras, IMRN (1999), # 5, 223-249.
(with I. Penkov) [PDF 353KB]
- Partially integrable highest weight modules, Transformation Groups 3 (1998), 241-253.
(with I. Penkov) [PDF 214KB]
- Partially and fully integrable modules over Lie superalgebras, Studies in Advanced Mathematics (series editor S.-T. Yau), 4, AMS and Internatl. Press 1997, 49-67.
(with I. Penkov) [PDF 315KB]
- Rational solutions to the Toda lattice hierarchy and irreducible representations of the Virasoro algebra, unpublished preprint, 1994, 13 pp.
[PDF 181KB]