2014/08/18 by Jon F. Carlson, Carlson, Jon F., Eric M. Friedlander +3
Mathematics · #16G10 #17B50 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:16G10 #msc:17B50
paper · pdf · doi:10.48550/arxiv.1408.3915
Replaces second half of arXiv:1207.5898 . To appear in Crelle
arxiv created 2014/08/18 · arxiv updated 2014/08/19
We introduce and investigate a functorial construction which associates coherent sheaves to finite dimensional (restricted) representations of a restricted Lie algebra \mathfrak g. These are sheaves on locally closed subvarieties of the projective variety \mathbb E(r,\mathfrak g) of elementary subalgebras of \mathfrak g of dimension r. We show that representations of constant radical or socle rank studied in \citeCFP3 which generalize modules of constant Jordan type lead to algebraic vector bundles on \mathbb E(r,\mathfrak g). For \mathfrak g = Lie(G), the Lie algebra of an algebraic group G, rational representations of G enable us to realize familiar algebraic vector bundles on G-orbits of \mathbb E(r, \mathfrak g).