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 Plus

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

Zendy Tools

Zendy Open

Recently E. Feigin introduced the $\mathbb G_a^N$-degenerations of semisimplealgebraic groups and their associated degenerate flag varieties. It has beenshown by Feigin, Finkelberg, and Littelmann that the degenerate flag varietiesin types $A_n$ and $C_n$ are Frobenius split. In this paper we construct anassociated degeneration of homogeneous coordinate rings of classical flagvarieties in all types and show that these rings are Frobenius split in mosttypes. It follows that the degenerate flag varieties of types $A_n$, $C_n$ and$G_2$ are Frobenius split. In particular we obtain an alternate proof ofsplitting in types $A_n$ and $C_n$; the case $G_2$ was not previously known. Wealso give a representation-theoretic condition on PBW-graded versions of Weylmodules which is equivalent to the existence of a Frobenius splitting of theclassical flag variety that maximally compatibly splits the identity.

Degenerate coordinate rings of flag varieties and Frobenius splitting