2018/09/24 by András C. Lőrincz, Michael D. Perlman, Lőrincz, András C. +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1809.08955
openalex publication_date 2018/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be the third exterior power of a six-dimensional complex vector space, equipped with the natural action of the group GL6(C) of invertible linear transformations of C6. We describe explicitly the category of GL6(C)-equivariant coherent DX-modules as the category of representations of a quiver with relations, which has finite representation type. We give a construction of the six simple equivariant DX-modules and give formulas for the characters of their underlying GL6(C)-structures. We describe the (iterated) local cohomology groups with supports given by orbit closures, determining, in particular, the Lyubeznik numbers associated to the orbit closures.