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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Semi-invariants of quivers and saturation for Littlewood-Richardson coefficients
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by Harm Derksen and Jerzy Weyman
J. Amer. Math. Soc. 13 (2000), 467-479
Published electronically: March 13, 2000


Let $Q$ be a quiver without oriented cycles. For a dimension vector $\beta$ let $\operatorname {Rep}(Q, \beta )$ be the set of representations of $Q$ with dimension vector $\beta$. The group $\operatorname {GL}(Q, \beta )$ acts on $\operatorname {Rep}(Q, \beta )$. In this paper we show that the ring of semi-invariants $\operatorname {SI} (Q,\beta )$ is spanned by special semi-invariants $c^V$ associated to representations $V$ of $Q$. From this we show that the set of weights appearing in $\operatorname {SI}(Q,\beta )$ 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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Bibliographic Information
  • Harm Derksen
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02151
  • Email:
  • Jerzy Weyman
  • Affiliation: Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
  • MR Author ID: 182230
  • ORCID: 0000-0003-1923-0060
  • Email:
  • 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.
  • © Copyright 2000 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 13 (2000), 467-479
  • MSC (2000): Primary 13A50; Secondary 14L24, 14L30, 16G20, 20G05
  • DOI:
  • MathSciNet review: 1758750