Proceedings of the American Mathematical Society

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



Double Koszul complex and construction of irreducible representations of $ \mathfrak{gl}(3\vert 1)$

Author: Nguyên Thi Phuong Dung
Journal: Proc. Amer. Math. Soc. 138 (2010), 3783-3796
MSC (2000): Primary 17B10, 17B70; Secondary 20G05, 20G42
Published electronically: May 24, 2010
MathSciNet review: 2679601
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Abstract: Let $ V$ be a super vector space with super dimension $ (m\vert 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\vert 1)$.

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Nguyên Thi Phuong Dung
Affiliation: Department of Algebra, Institute of Mathematics, VAST, 18 Hoang Quôc Viet Road, CauGiay, 10307, Ha Noi, Viet Nam

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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.