Steinberg Modules and Donkin Pairs
نویسنده
چکیده
We prove that in characteristic p > 0 a module with good filtration for a group of type E6 restricts to a module with good filtration for a group of type F4. Thus we confirm a conjecture of Brundan for one more case. Our method relies on the canonical Frobenius splittings of Mathieu. Next we settle the remaining cases, in characteristic not 2, with a computer-aided variation on the old method of Donkin.
منابع مشابه
6 A ug 1 99 9 Steinberg modules and Donkin pairs
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). I...
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