sider the direct image of the constant sheaf 0£'.

20. 13. 10 and let L 1 < f. We define L' = L®L~n. ). It is clear that WLn=WL'n• SLn=SL'n• RLn=RL'n· ' ' ' ' ' ' Let M be the fiber product L. x L~. We define maps a: M g) (3: M -> -> L 0 , (L')° by a(e, e 1) = e, {3(e, e1) = e®(e~n). We have natural actions of H = U x k* on L. and (L'). 4). ,n . The space M has two actions of U x k* x k*. For both actions, u < U acts by u: (e, e1) -. (ue, ue 1). An element (x,y) < k* x k* acts by ce, el) -> (xne, y- 1e1)' for the first action ce, el) -> (xnyne,y- 1e11' for the second action.

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Characters of Reductive Groups over a Finite Field by George Lusztig


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