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/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $G$ be a complex reductive group and $P$ be a parabolic subgroup of $G$.In this paper the authors address questions involving the realization of the$G$-module of the global sections of the (twisted) cotangent bundle over theflag variety $G/P$ via the cohomology of the small quantum group. Our mainresults generalize the important computation of the cohomology ring for thesmall quantum group by Ginzburg and Kumar, and provides a generalization ofwell-known calculations by Kumar, Lauritzen, and Thomsen to the quantum caseand the parabolic setting. As an application we answer the question (firstposed by Friedlander and Parshall for Frobenius kernels) about the realizationof coordinate rings of Richardson orbit closures for complex semisimple groupsvia quantum group cohomology. Formulas will be provided which relate themultiplicities of simple $G$-modules in the global sections with the dimensionsof extension groups over the large quantum group.

Realizing Rings of Regular Functions via the Cohomology of Quantum Groups