Rational smoothness of varieties of representations for quivers of Dynkin type

Details Rational smoothness of varieties of representations for quivers of Dynkin type Rational smoothness of varieties of representations for quivers of Dynkin type

2003-05-09

arxiv.org/abs/math/0305149v1

Mathematics

Representation Theory

15 pages

Scientific paper

With the help of Lusztig's canonical basis, we study local intersection cohomology of the Zariski closures of orbits of representations of a quiver of type A, D or E. In particular, we characterize the rationally smooth orbits and prove that orbit closures are smooth if and only if they are rationally smooth. This provides an analogue of theorems of V. Deodhar, and J. Carrell and D. Peterson on Schubert varieties.

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