On the 2-modular reduction of the Steinberg representation of the symplectic group
Fernando Szechtman
math.RTarXiv:math/0212378
Abstract
We show that in characteristic 2, the Steinberg representation of the symplectic group Sp(2n,q), q a power of an odd prime p, has two irreducible constituents lying just above the socle that are isomorphic to the two Weil modules of degree (qn-1)/2.
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