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In this paper, we carry out several computations involving graded (or Gm-equivariant) perversecoherent sheaves on the nilpotent cone of a reductive group in good characteristic. In the first part of the paper, we compute the weight of the Gm-action on certain normalized (or 'canonical') simple objects, confirming an old prediction of Ostrik. In the second part of the paper, we explicitly describe all simple perverse-coherent sheaves for G = PGL3, in every characteristic other than 2 or 3. Applications include an explicit description of the cohomology of tilting modules for the corresponding quantum group, as well as a proof that PCohGm(N) never admits a positive grading when the characteristic of the field is greater than 3.

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Quarterly Journal of Mathematics

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