We describe a cluster algebra algorithm for calculating -characters of Kirillov–Reshetikhin modules for any untwisted quantum affine algebra . This yields a geometric -character formula for tensor products of Kirillov–Reshetikhin modules. When is of type , this formula extends Nakajima's formula for -characters of standard modules in terms of homology of graded quiver varieties.
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David Hernandez, Bernard Leclerc, A cluster algebra approach to -characters of Kirillov–Reshetikhin modules. J. Eur. Math. Soc. 18 (2016), no. 5, pp. 1113–1159DOI 10.4171/JEMS/609