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Journal of the London Mathematical Society Advance Access originally published online on August 27, 2007
Journal of the London Mathematical Society 2007 76(1):135-147; doi:10.1112/jlms/jdm043
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© 2007 London Mathematical Society

On the number of subrepresentations of a general quiver representation

Harm Derksen

Department of Mathematics
University of Michigan
530 Church Street
Ann Arbor, MI 48109-1043
USA

Aidan Schofield

School of Mathematics
University of Bristol
Clifton, Bristol, Avon
BS8 1TW
UK
Aidan.Schofield{at}bristol.ac.uk

Jerzy Weyman

Department of Mathematics
Northeastern University
360 Huntington Avenue
Boston, MA 02115
USA
j.weyman{at}neu.edu

It is well known that the intersection multiplicities of Schubert classes in the Grassmannian are Littlewood–Richardson coefficients. We generalize this statement in the context of quiver representations. Here the intersection multiplicity of Schubert classes is replaced by the number of subrepresentations of a general quiver representation, and the Littlewood–Richardson coefficients are replaced by the dimension of a certain space of semi-invariants.

hderksen{at}umich.edu

2000 Mathematics Subject Classification 13A50, 14M15, 16G20.

The first author was supported by NSF grant DMS 0349019 and the third by NSF grant DMS 0300064.

Received January 24, 2006; revised October 4, 2006; published online August 27, 2007.


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