English

On the cardinalities of Kronecker quiver Grassmannians

Representation Theory 2009-09-25 v2

Abstract

We deduce using the Ringel-Hall algebra approach explicit formulas for the cardinalities of some Grassmannians over a finite field associated to the Kronecker quiver. We realize in this way a quantification of the formulas obtained by Caldero and Zelevinsky for the Euler characteristics of these Grassmannians. We also present a recursive algorithm for computing the cardinality of every Kronecker quiver Grassmannian over a finite field.

Keywords

Cite

@article{arxiv.0903.1928,
  title  = {On the cardinalities of Kronecker quiver Grassmannians},
  author = {Csaba Szántó},
  journal= {arXiv preprint arXiv:0903.1928},
  year   = {2009}
}

Comments

Major corrections and completions were made. We also present a recursive algorithm for computing the cardinality of every Kronecker quiver Grassmannian over a finite field