On the fermionc formula and the Kirillov-Reshetikhin conjecture

Details On the fermionc formula and the Kirillov-Reshetikhin conjecture On the fermionc formula and the Kirillov-Reshetikhin conjecture

2000-06-12

arxiv.org/abs/math/0006090v2

Mathematics

Quantum Algebra

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

Scientific paper

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 $W(m\lambda_i)$ of the corresponding quantum affine algebras. In this paper, we show that the conjecture is true for the modules W(m\lambda_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.

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