Advances in Representation Theory of Algebras

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pp: 211–230

DOI: 10.4171/125-1/7

Cluster algebras and singular supports of perverse sheaves

Hiraku Nakajima[1]

(1) Research Institute for Mathematical Sciences, Kyoto University, 606-8502, KYOTO, JAPAN

We propose an approach to Geiss–Leclerc–Schroer’s conjecture on the cluster algebra structure on the coordinate ring of a unipotent subgroup and the dual canonical base. It is based on singular supports of perverse sheaves on the space of representations of a quiver, which give the canonical base.

Keywords: Cluster algebras, perverse sheaves, singular supports