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; Supergeometry. For more details, see some of my papers below.

Ind-varieties of generalized flags as homogeneous spaces for classical ind--groups, preprint, 2001, 14 pp. (with I. Penkov) [PDF] 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] On the structure of weight modules, Transactions AMS 352 (2000), 2857-2869. (with O. Mathieu and I. Penkov)[PDF] Weight modules of direct limit Lie algebras, IMRN (1999), # 5, 223-249. (with I. Penkov)[PDF] Partially integrable highest weight modules, Transformation Groups 3 (1998), 241-253. (with I. Penkov)[PDF] 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Penkov)[PDF] Rational solutions to the Toda lattice hierarchy and irreducible representations of the Virasoro algebra, unpublished preprint, 1994, 13 pp.[PDF]