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

David Hernandez, Bernard Leclerc (2016)

Journal of the European Mathematical Society

We describe a cluster algebra algorithm for calculating q -characters of Kirillov–Reshetikhin modules for any untwisted quantum affine algebra U q ( 𝔤 ^ ) . This yields a geometric q -character formula for tensor products of Kirillov–Reshetikhin modules. When 𝔤 is of type A , D , E , this formula extends Nakajima’s formula for q -characters of standard modules in terms of homology of graded quiver varieties.

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