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Cohomology of line bundles on the flag variety for type G_2

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  • Henning Haahr Andersen, Denmark
  • Masaharu Kaneda, Osaka City University, Japan
In the case of a simple algebraic group G of type G2 over a field of characteristic p>0 we study the cohomology modules of line bundles on the flag variety for G. Our main result is a complete determination of the vanishing behavior of such cohomology in the case where the line bundles in question are induced by characters from the lowest p2-alcoves.

When Uq is the quantum group corresponding to G whose parameter q is a complex root of unity of order prime to 6 we give a complete (i.e. covering all characters) description of the vanishing behavior for the corresponding quantized cohomology modules.
Original languageEnglish
JournalJournal of Pure and Applied Algebra
Volume216
Issue7
Pages (from-to)1566-1579
Number of pages14
ISSN0022-4049
DOIs
Publication statusPublished - 2012

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