English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

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.

Calculations with graded perverse-coherent sheaves