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Lusztig conjecture:

H.H. Andersen, J.C. Jantzen, W. Soergel,
Representations of quantum groups at a $p$th root of unity and of
semisimple groups in characteristic $p$, Ast\'erisque, 220, (1994).

Non-defining characteristic:

M. Geck and G. Hiss, Modular representations of finite groups of Lie type in non-defining characteristic, in Prog. Math. 141, Birkhauser (1997).

Magma:

W. Bosma, J. Cannon, Handbook on Magma Functions, Sydney
University, 1996.

W. Bosma, J. Cannon, C. Playhoust, The Magma Algebra System I: The
User Language, J. Symbolic Computation, 3/4, no. 24 (1997), 235-265.

Examples of Computation:

University of Georgia VIGRE Algebra Group:

1) Varieties of nilpotent elements for simple Lie algebras I: good
primes, J. Algebra, 280 (2004), 719--737.

2) Varieties of nilpotent elements for simple Lie algebras II: bad
primes, J. Algebra, 292 (2005), 65--99.

3) Support varieties for Weyl modules over bad primes, J. Algebra,
312 (2007), 602--633.



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