Steinberg modules and Donkin pairs

Details Steinberg modules and Donkin pairs Steinberg modules and Donkin pairs

1999-08-06

arxiv.org/abs/math/9908026v3

Transformation Groups, Vol. 6, No. 1, 2001, pp. 87-98

Mathematics

Representation Theory

16 pages; proof of Brundan's conjecture added

Scientific paper

10.1007/BF01236064

We prove that in positive characteristic a module with good filtration for a group of type E6 restricts to a module with good filtration for a subgroup of type F4. (Recall that a filtration of a module for a semisimple algebraic group is called good if its layers are dual Weyl modules.) Our result confirms a conjecture of Brundan for one more case. The 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.

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