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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Double Koszul complex and construction of irreducible representations of $\mathfrak {gl}(3|1)$
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by Nguyễn Thi Phuong Dung PDF
Proc. Amer. Math. Soc. 138 (2010), 3783-3796 Request permission


Let $V$ be a super vector space with super dimension $(m|n)$. Manin introduced the Koszul complex associated to $V$, which is denoted $K$. There is another Koszul complex, denoted $L$. Our observation is that these two Koszul complexes can be combined into a double complex, which we call the double Koszul complex. By using the differential of this complex, we give a way to describe all irreducible representations of $\frak {gl}(V)$ when $V$ has super dimension $(3|1)$.
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Additional Information
  • Nguyễn Thi Phuong Dung
  • Affiliation: Department of Algebra, Institute of Mathematics, VAST, 18 Hoang Quôc Viet Road, CauGiay, 10307, Ha Noi, Viet Nam
  • Email:
  • Received by editor(s): October 15, 2009
  • Received by editor(s) in revised form: January 21, 2010
  • Published electronically: May 24, 2010
  • Additional Notes: Financial support provided to the author by NAFOSTED under grant no.
  • Communicated by: Martin Lorenz
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 138 (2010), 3783-3796
  • MSC (2000): Primary 17B10, 17B70; Secondary 20G05, 20G42
  • DOI:
  • MathSciNet review: 2679601