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The geometric small property (Borho-MacPherson [2]) of projective morphisms implies a description of their singularities in terms of intersection homology. In this paper we solve the smallness problem raised by Nakajima [37, 35] for certain resolutions of quiver varieties [37] (analogs of the Springer resolution): for Kirillov-Reshetikhin modules of simply-laced quantum affine algebras, we characterize explicitly the Drinfeld polynomials corresponding to the small resolutions. We use an elimination...
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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