JournalsjemsVol. 18, No. 5pp. 1113–1159

A cluster algebra approach to qq-characters of Kirillov–Reshetikhin modules

  • David Hernandez

    Université Paris Diderot – Paris 7, Paris Rive Gauche, France
  • Bernard Leclerc

    Université de Caen, France
A cluster algebra approach to $q$-characters of Kirillov–Reshetikhin modules cover
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Abstract

We describe a cluster algebra algorithm for calculating qq-characters of Kirillov–Reshetikhin modules for any untwisted quantum affine algebra Uq(g^)U_q(\widehat{\mathfrak{g}}). This yields a geometric qq-character formula for tensor products of Kirillov–Reshetikhin modules. When g\mathfrak g is of type A,D,EA, D, E, this formula extends Nakajima's formula for qq-characters of standard modules in terms of homology of graded quiver varieties.

Cite this article

David Hernandez, Bernard Leclerc, A cluster algebra approach to qq-characters of Kirillov–Reshetikhin modules. J. Eur. Math. Soc. 18 (2016), no. 5, pp. 1113–1159

DOI 10.4171/JEMS/609