Bases of representations of type A affine Lie algebras via q(17)

We relate two apparently different bases in the representations of affine Lie algebras of type A: one arising from statistical mechanics, the other from gauge theory. We show that the two are governed by the same combinatorics and therefore can be viewed a

AFFINELIEALGEBRAS,QUIVERVARIETIESANDSTATISTICALMECHANICS17ofYiandYi 1numberedli+1andaboveareequal.Thenbyconsideringthecases

i 1≥bi,weseethat ∞ 1ifi 1i 1ij(H(λij,λj+1) H(λj,λj+1))=ai+

j=1