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Nov 14, 2016 at 16:46 comment added Mathew There is a natural action of the Weyl group (In this case its $S_n$) on the zero weight space that is the $T$ invariants of the Global sections of of the line bundle $L_{2\rho}$ on $G/B$ which has a basis of standard tableaux with some restriction on entries. What is this action ?
Oct 15, 2016 at 23:35 history answered Allen Knutson CC BY-SA 3.0