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- W2912129491 abstract "We introduce the alternating Schur algebra $AS_F(n,d)$ as the commutant of the action of the alternating group $A_d$ on the $d$-fold tensor power of an $n$-dimensional $F$-vector space. When $F$ has characteristic different from $2$, we give a basis of $AS_F(n,d)$ in terms of bipartite graphs, and a graphical interpretation of the structure constants. We introduce the abstract Koszul duality functor on modules for the even part of any $mathbf Z/2mathbf Z$-graded algebra. The algebra $AS_F(n,d)$ is $mathbf Z/2mathbf Z$-graded, having the classical Schur algebra $S_F(n,d)$ as its even part. This leads to an approach to Koszul duality for $S_F(n,d)$-modules that is amenable to combinatorial methods. We characterize the category of $AS_F(n,d)$-modules in terms of $S_F(n,d)$-modules and their Koszul duals. We use the graphical basis of $AS_F(n,d)$ to study the dependence of the behavior of derived Koszul duality on $n$ and $d$." @default.
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- W2912129491 date "2020-06-14" @default.
- W2912129491 modified "2023-09-27" @default.
- W2912129491 title "Schur algebras for the alternating group and Koszul duality" @default.
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- W2912129491 doi "https://doi.org/10.2140/pjm.2020.306.153" @default.
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