Proof of the combinatorial Kirillov-Reshetikhin conjecture

Details Proof of the combinatorial Kirillov-Reshetikhin conjecture Proof of the combinatorial Kirillov-Reshetikhin conjecture

2007-10-24

arxiv.org/abs/0710.4415v2

Mathematics

Quantum Algebra

36 pages. Corrected version for publication

Scientific paper

In this paper we give a direct proof of the equality of certain generating function associated with tensor product multiplicities of Kirillov-Reshetikhin modules for each simple Lie algebra g. Together with the theorems of Nakajima and Hernandez, this gives the proof of the combinatorial version of the Kirillov-Reshetikhin conjecture, which gives tensor product multiplicities in terms of restricted fermionic summations.

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