Distinguished bases for A_n root systems and parking functions

Details Distinguished bases for A_n root systems and parking functions Distinguished bases for A_n root systems and parking functions

2011-12-02

arxiv.org/abs/1112.0381v1

Mathematics

Representation Theory

29 pages

Scientific paper

A well-known result of O. Lyashko and E. Looijenga states that the number of the distinguished bases for A_n singularity equals to (n+1)^{n-1}. We give a combinatorial description of these bases by constructing an explicit bijection with the set of parking functions on n elements. We describe the induced action of the braid group on parking functions. We investigate links of these constructions to exceptional sequences in the category of representations of the Dynkin quiver A_n with linear orientation.

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