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Cohomology of Line Bundles on the Flag Variety for Type G_2
In the case of an almost simple algebraic group of type over a
field of characteristic we study the cohomology modules of line bundles
on the flag variety for . 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 -alcoves.
When is the quantum group corresponding to whose parameter 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
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