6 A ug 1 99 9 Steinberg modules and Donkin pairs
نویسنده
چکیده
Now choose a Borel subgroup B in G and a maximal torus T in B so that, if B is the opposite Borel subgroup, then B ∩ H and B ∩ H are a Borel subgroups in H and T ∩H is a maximal torus in H . We follow the convention that the roots of B are positive. If λ ∈ X(T ), then indGB(−λ) is the dual Weyl module ∇G(λ ) with highest weight λ = −w0λ and lowest weight −λ. Its dual is the Weyl module ∆G(λ). In a good filtration of a G-module the layers are of the form ∇G(μ). Let U(U) denote the hyperalgebra of the unipotent radical U of B. We recall the presentation of Weyl modules.
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Steinberg Modules and Donkin Pairs
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