gh-36724: Compute dimensions of simple symmetric group modules over positive characteristic
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We can compute Specht module dimensions, but an interesting open problem
is to compute the dimensions of simple modules for `S_n` over fields of
positive characteristic. We provide a way to compute dimensions by using
the pullback of the polytabloid inner product and computing the rank of
the Gram matrix.
This is based off of code provided by Jackson Walters.
We also implement a more efficient column stabilizer method for standard
tableaux.
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URL: https://github.com/sagemath/sage/pull/36724
Reported by: Travis Scrimshaw
Reviewer(s): Frédéric Chapoton, Travis Scrimshaw
