Mathematics – Quantum Algebra
Scientific paper
2005-01-11
Mathematics
Quantum Algebra
22 pages
Scientific paper
Let Q be an affine quiver of type A. Let C be the associated generalized Cartan matrix. Let U^- be the negative part of the quantized enveloping algebra attached to C. In terms of perverse sheaves on the moduli space of representations of a quiver, Lusztig constructed U geometrically and gave a canonical basis B of U^- at the same time. The simple perverse sheaves which enter B are defined abstractly in general. In Lusztig's paper [L2], by using McKay's correspondence, he gave a description of these canonical basis elements in affine cases, i.e. specifying the corresponding supports and local systems. But the chosen orientations and the number of vertices of the quiver are not arbitrary. In this paper we generalized the description in [L2] for arbitrary orientations and vertices in the case of type A by using the theory of representations of quivers.
No associations
LandOfFree
Affine quivers of type A and canonical bases 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 Affine quivers of type A and canonical bases, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Affine quivers of type A and canonical bases will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-179720