Geodesic
Orthosymplectic Lie superalgebras, Koszul duality, and a complete intersection analogue of the Eagon–Northcott complex
Journal of the European Mathematical Society, Tome 18 (2016) no. 12, pp. 2691-2732 Cet article a éte moissonné depuis la source EMS Press

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We study the ideal of maximal minors in Littlewood varieties, a class of quadratic complete intersections in spaces of matrices. We give a geometric construction for a large class of modules, including all powers of this ideal, and show that they have a linear free resolution over the complete intersection and that their Koszul dual is an infinite-dimensional irreducible representation of the orthosymplectic Lie superalgebra. We calculate the algebra of cohomology operators acting on this free resolution. We prove analogous results for powers of the ideals of maximal minors in the variety of length 2 complexes when it is a complete intersection, and show that their Koszul dual is an infinite-dimensional irreducible representation of the general linear Lie superalgebra.
DOI : 10.4171/jems/651
Classification : 13-XX, 17-XX, 18-XX
Keywords: Complete intersections, minimal free resolutions, classical Lie superalgebras, Koszul duality, Howe duality 
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     author = {Steven V Sam},
     title = {Orthosymplectic {Lie} superalgebras, {Koszul} duality, and a complete intersection analogue of the {Eagon{\textendash}Northcott} complex},
     journal = {Journal of the European Mathematical Society},
     pages = {2691--2732},
     year = {2016},
     volume = {18},
     number = {12},
     doi = {10.4171/jems/651},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/651/}
}
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Steven V Sam. Orthosymplectic Lie superalgebras, Koszul duality, and a complete intersection analogue of the Eagon–Northcott complex. Journal of the European Mathematical Society, Tome 18 (2016) no. 12, pp. 2691-2732. doi: 10.4171/jems/651

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