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This paper provides a brief review of the relations between the Feigin-Loktevconjecture on the dimension of graded tensor products of $\g[t]$-modules, theKirillov-Reshetikhin conjecture, the combinatorial ``M=N" conjecture, theirproofs for all simple Lie algebras, and a pentagon of identities which resultsfrom the proof.

A pentagon of identities, graded tensor products and the Kirillov-Reshetikhin conjecture