Beyond Kirillov-Reshetikhin modules

Details Beyond Kirillov-Reshetikhin modules Beyond Kirillov-Reshetikhin modules

2008-12-09

arxiv.org/abs/0812.1716v2

Contemp. Math. 506 (2010), 49-81

Mathematics

Quantum Algebra

35 pages

Scientific paper

In this survey, we shall be concerned with the category of finite-dimensional representations of the untwisted quantum affine algebras when the quantum parameter q is not a root of unity. We review the foundational results of the subject, including the Drinfeld presentation, the classification of simple modules and q-characters. We then concentrate on particular families of irreducible representations whose structure has recently been understood: Kirillov-Reshetikhin modules, minimal affinizations and beyond.

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