REPRESENTATION
THEORY AND RELATED TOPICS SEMINAR
ABSTRACT: Generalized
Weyl algebras (GWAs), including down-up algebras and their quantum
variants, have been the focus of much recent activity. In recent work,
we show that a large family of generalized down-up algebras, which are
deformations of sl_2, admit quantizations which are deformations of
quantum sl_2.
Next, we study the BGG Category O over a triangular
GWA, specifically, blocks with finitely many simple objects. We show
that the endomorphism algebra of a projective generator of such a block
is finite-dimensional and graded Koszul. We also show how blocks of O
categorify Young diagrams, by studying projectives and tilting objects
in detail. (Partly joint with Akaki Tikaradze.)
For further information visit http://www.northeastern.edu/martsinkovsky/p/rtrt.html or contact Alex Martsinkovsky alexmart >at< neu >dot< edu