2002/11/30 by Igor Frenkel, Igor B. Frenkel, Alistair Savage · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #math.AG #math.RT #msc:16G20 #msc:17B65 #msc:82B23
paper · pdf · doi:10.1155/s1073792803211284
published as Inter. Math. Res. Notices, 28 (2003), p. 1521-1547 · 19 pages. v2: minor typos corrected
openalex publication_date 2003/01/01 · arxiv created 2003/03/14 · arxiv updated 2012/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We relate two apparently different bases in the representations of affine Lie algebras of type A: one arising from statistical mechanics and the other from gauge theory. We show that the two are governed by the same combinatorics that also respects the weight space decomposition of the representations. In particular, we are able to give an alternative and much simpler geometric proof of the main result of E. Date et al. (1989) on the construction of bases of affine Lie algebra representations. At the same time, we give a simple parametrization of the irreducible components of Nakajima quiver varieties associated to infinite and cyclic quivers. We also define new varieties whose irreducible components are in one-to-one correspondence with the highest weight representations of ℊℓn+1.