NORTHEASTERN UNIVERSITY
MATHEMATICS DEPARTMENT

REPRESENTATION THEORY AND RELATED TOPICS SEMINAR


  Apoorva Khare
(Stanford, CA)


The BGG Category O over Generalized Weyl Algebras

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.)


October 23, 2015
11:00 - 12:00
(Notice unusual time)
511 Lake Hall


For further information visit http://www.northeastern.edu/martsinkovsky/p/rtrt.html  or contact Alex Martsinkovsky alexmart >at< neu >dot< edu