Mathematics – Representation Theory
Scientific paper
2008-11-13
Mathematics
Representation Theory
This is a MUCH expanded, improved, and generalized version of a previous preprint - arXiv:math/0502227; 31 pages, laTeX, submi
Scientific paper
The main goal of this paper is to show that a wide variety of infinite-dimensional algebras all share a common structure, including a triangular decomposition and a theory of weights. This structure allows us to define and study the BGG Category O, generalizing previous definitions of it. Having presented our axiomatic framework, we present sufficient conditions that guarantee finite length, enough projectives, and a block decomposition into highest weight categories. The framework is strictly more general than the usual theory of O; this is needed to accommodate (quantized or higher rank) infinitesimal Hecke algebras, in addition to semisimple Lie algebras and their quantum groups. We then present numerous examples, two families of which are studied in detail. These are quantum groups defined using not necessarily the root or weight lattices (for these, we study the center and central characters), and infinitesimal Hecke algebras.
No associations
LandOfFree
Axiomatic framework for the BGG Category O does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Axiomatic framework for the BGG Category O, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Axiomatic framework for the BGG Category O will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-435306