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- Title
Calculations with graded perverse-coherent sheaves.
- Authors
Achar, Pramod N; Hardesty, William D
- Abstract
In this paper, we carry out several computations involving graded (or |${{\mathbb {G}}_{\textrm {m}}}$| -equivariant) perverse-coherent 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 |${{\mathbb {G}}_{\textrm {m}}}$| -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 |$G = PGL_3$| , 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 |$\textsf {PCoh}^{{{\mathbb {G}}_{\textrm {m}}}}({\mathcal {N}})$| never admits a positive grading when the characteristic of the field is greater than 3.
- Subjects
SHEAF theory; QUANTUM groups
- Publication
Quarterly Journal of Mathematics, 2019, Vol 70, Issue 4, p1327
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmath/haz016