Document Type
Article
Publication Date
12-1-2019
Abstract
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.
Publication Source (Journal or Book title)
Quarterly Journal of Mathematics
First Page
1327
Last Page
1352
Recommended Citation
Achar, P., & Hardesty, W. (2019). Calculations with graded perverse-coherent sheaves. Quarterly Journal of Mathematics, 70 (4), 1327-1352. https://doi.org/10.1093/qmath/haz016
