Double Koszul complex and construction of irreducible representations of $\mathfrak {gl}(3|1)$
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Abstract:
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 $(3|1)$.References
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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: phuongdung72@yahoo.com
- 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. 101.01.16.09
- 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: https://doi.org/10.1090/S0002-9939-2010-10400-8
- MathSciNet review: 2679601