Kirillov-Reshetikhin modules associated to G2

摘要

In this paper study the modules for the current algebra associated to G2-^sThese were defined in [2]. We also define and study the modules for the twisted current algebra associated to D4 and a diagram automorphism of order three. In both cases the fixed point subalgebra go is of type G2 We prove that the conjectures of [7] and [8] are true in these cases. In particular, there are now maps of go-modules between the distinct non-zero graded pieces for KRa{rnu)i) for some i and the multiplicity of an irreducible module in a graded piece can be greater than one. Moreover, our result on the graded character of the module KR(mu)i) for G2 is actually an improvement on the conjectural graded-character formula in [7]. This is because the formulas given in [7] have terms occurring with zero multiplicity.