Cohomology of Line Bundles on the Flag Variety for Type G₂

2011/07/15 by Andersen, Henning Haahr, Kaneda, Masaharu
#14M15 #17B37 #20G05 #20G10 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1107.3055

Abstract

In the case of an almost 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 U_q 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.

Related

• Some questions arising from the study of cohomology on flag varieties
• Representation Theory via Cohomology of Line Bundles
• Cohomology of Line Bundles on the Incidence Correspondence
• On the cohomology of line bundles over certain flag schemes
• Quantum cohomology of flag varieties