Socle Series of Cohomology Groups of Line Bundles on G/B Short running title: Socle Series of Cohomology Groups
نویسنده
چکیده
The G-module structure of the cohomology groups of line bundles over the flag variety G/B for a semisimple algebraic group G is studied. It is proved that, generically, their socle filtrations satisfy the same sum formula as Andersen’s filtrations if Lusztig’s conjecture is true. Another purpose of this paper is to calculate the socle series of the H0’s for the p-regular weights close to a chamber wall for the group of type G2, because the multiplicity is not free in this case. Introduction Let G be a connected and simply connected semisimple algebraic group over an algebraically closed field of characteristic p > 0 and B a Borel subgroup of G. The cohomology group H (λ) of the line bundle on the flag variety G/B induced from a character λ of B has a G-module structure in a natural way. Weyl modules are precisely the nonvanishing H(λ), where N = dimG/B. In fact, the Weyl modules are the dual modules of the nonvanishing induced modules H(λ). In this paper we study the socle series of H (λ) as G-module. Concerning the structure of Weyl modules, Jantzen [14] constructed a filtration via a contravariant form. This filtration satisfies a certain sum formula of characters. More recent investigations give more evidence that the Jantzen filtration is the 1980 Mathematics Subject Classification (1985 Revision) Primary 20G05
منابع مشابه
Structure of Cohomology of Line Bundles on G/B for Semisimple Groups Short running title: Cohomology of Line Bundles
Let G be a connected and simply connected semisimple algebraic group over an algebraically closed field k of characteristic p > 0, T a maximal torus of G and B a Borel subgroup containing T . Each weight in X(T ) determines a line bundle on the flag varietyG/B. It turns out that cohomology of the line bundle is isomorphic to the derived functor of the induction functors from the category of B-m...
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