Double Koszul complex and construction of irreducible representations of 𝔤𝔩(3|1)

Dung, Nguyễn

doi:10.1090/S0002-9939-2010-10400-8

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

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 $(3|1)$.

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