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

The Gelfand-Tsetlin and the Feigin-Fourier-Littelmann-Vinberg polytopes forthe Grassmannians are defined, from the perspective of representation theory,to parametrize certain bases for highest weight irreducible modules. Thesepolytopes are Newton-Okounkov bodies for the Grassmannian and, in particular,the GT-polytope is an example of a string polytope. The polytopes admit acombinatorial description as the Stanley's order and chain polytopes of acertain poset, as shown by Ardila, Bliem and Salaza. We prove that thesepolytopes occur among matching field polytopes. Moreover, we show that they arerelated by a sequence of combinatorial mutations that passes only throughmatching field polytopes. As a result, we obtain a family of matching fieldsthat give rise to toric degenerations for the Grassmannians. Moreover, allpolytopes in the family are Newton-Okounkov bodies for the Grassmannians.

Combinatorial Mutations of Gelfand-Tsetlin Polytopes, Feigin-Fourier-Littelmann-Vinberg Polytopes, and Block Diagonal Matching Field Polytopes