Semi-invariants of quivers and saturation for Littlewood-Richardson coefficients

Authors:
Harm Derksen and Jerzy Weyman

Journal:
J. Amer. Math. Soc. **13** (2000), 467-479

MSC (2000):
Primary 13A50; Secondary 14L24, 14L30, 16G20, 20G05

DOI:
https://doi.org/10.1090/S0894-0347-00-00331-3

Published electronically:
March 13, 2000

MathSciNet review:
1758750

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Let be a quiver without oriented cycles. For a dimension vector let be the set of representations of with dimension vector . The group acts on . In this paper we show that the ring of semi-invariants is spanned by special semi-invariants associated to representations of . From this we show that the set of weights appearing in is saturated. In the case of triple flag quiver this reduces to the results of Knutson and Tao on the saturation of the set of triples of partitions for which the Littlewood-Richardson coefficient is nonzero.

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Additional Information

**Harm Derksen**

Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02151

Email:
hderksen@math.mit.edu

**Jerzy Weyman**

Affiliation:
Department of Mathematics, Northeastern University, Boston, Massachusetts 02115

Email:
weyman@neu.edu

DOI:
https://doi.org/10.1090/S0894-0347-00-00331-3

Keywords:
Quiver representations,
semi-invariants,
Littlewood-Richardson coefficients,
Klyachko cone,
saturation

Received by editor(s):
July 20, 1999

Published electronically:
March 13, 2000

Additional Notes:
The second author was supported by NSF, grant DMS 9700884 and KBN No. PO3A 012 14.

Article copyright:
© Copyright 2000
American Mathematical Society