On the fermionc formula and the Kirillov-Reshetikhin conjecture

Abstract

The fermionic formula conjectured by Kirillov and Reshetikhin describes the decomposition (as a module for $U_q(\frak g)$) of a tensor product of multiples of of fundamental representations $W(mλ_i)$ of the corresponding quantum affine algebras. In this paper, we show that the conjecture is true for the modules W(mλ_i), if $i$ is such that the corresponding simple root occurs in the highest root of the simple Lie algebra with multiplicity at most 2. In particular, the conjecture is established for all but a few nodes for the exceptional algebras.

The paper has been extensively rewritten and now includes a proof in the case of non--simply laced algebras as well