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

Mathematics – Quantum Algebra

Scientific paper

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21 pages

Scientific paper

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

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