Quivers, desingularizations and canonical bases

Details Quivers, desingularizations and canonical bases Quivers, desingularizations and canonical bases

2001-04-30

arxiv.org/abs/math/0104284v1

Mathematics

Algebraic Geometry

22 pages

Scientific paper

A class of desingularizations for orbit closures of representations of Dynkin quivers is constructed, which can be viewed as a graded analogue of the Springer resolution. A stratification of the singular fibres is introduced; its geometry and combinatorics are studied. Via the Hall algebra approach, these constructions relate to bases of quantized enveloping algebras. Using Ginzburg's theory of convolution algebras, the base change coefficients of Lusztig's canonical basis are expressed as decomposition numbers of certain convolution algebras.

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