Constructing equivariant vector bundles via the BGG correspondence. (March 2019)

• Record Type: Journal Article
• Authors: Posur, Sebastian
• Is Part Of: Journal of symbolic computation. Volume 91(2019)
• Page Start: 57
• Page End: 73
• Publication Date: 2019-03
• Subjects: 14F05 -- 16E05 -- 16E20; BGG correspondence -- Equivariant vector bundle -- Grothendieck group -- Cohomology table; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2018.06.013
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We describe a strategy for the construction of finitely generated G -equivariant Z -graded modules M over the exterior algebra for a finite group G . By an equivariant version of the BGG correspondence, M defines an object F in the bounded derived category of G -equivariant coherent sheaves on projective space. We develop a necessary condition for F being isomorphic to a vector bundle that can be simply read off from the Hilbert series of M . Combining this necessary condition with the computation of finite excerpts of the cohomology table of F makes it possible to enlist a class of equivariant vector bundles on P 4 that we call strongly determined in the case where G is the alternating group on 5 points.