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

By Bernard Leclerc, D. Hernandez. 2013

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We describe a cluster algebra algorithm for calculating q-characters of Kirillov-Reshetikhin modules for any untwisted quantum affine algebra. This yields a geometric q-character formula for tensor products of Kirillov-Reshetikhin modules. In simply laced type this formula extends Nakajima's formula for q-characters of standard modules in terms of homology of graded quiver varieties.

Subfields: Algebra and Number Theory, Artificial Intelligence, Geometry and Topology

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