Max-Planck-Insitut fuer Mathematik
Vivatsgasse 7, D-53111 Bonn, Germany
 E-mail: vybornov@mpim-bonn.mpg.de

Affine Lie algebras, quiver varieties, and algebras of BPS states
 
Abstract:
C.M. Ringel defined Hall algebra associated with the category of representations of a quiver of Dynkin type and gave an explicit description of the structure constants of the corresponding Lie algebra. Jointly with I. Frenkel and A. Malkin we generalized Ringel's result to the case of a quiver of affine type.
In this talk we will discuss the combinatorial questions arising from this subject, in particular calculation of some elements of transition matrix between a PBW basis and Lusztig's (semi)canonical basis.
We will also explain how to construct the Lie algebra of BPS states at the orbifold point using our methods in terms of quivers.