Skip to Main Content

Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Reflexivity of Newton–Okounkov bodies of partial flag varieties
HTML articles powered by AMS MathViewer

by Christian Steinert
Represent. Theory 26 (2022), 859-873
Published electronically: August 16, 2022


Assume that the valuation semigroup $\Gamma (\lambda )$ of an arbitrary partial flag variety corresponding to the line bundle $\mathcal {L_\lambda }$ constructed via a full-rank valuation is finitely generated and saturated. We use Ehrhart theory to prove that the associated Newton–Okounkov body — which happens to be a rational, convex polytope — contains exactly one lattice point in its interior if and only if $\mathcal {L}_\lambda$ is the anticanonical line bundle. Furthermore, we use this unique lattice point to construct the dual polytope of the Newton–Okounkov body and prove that this dual is a lattice polytope using a result by Hibi. This leads to an unexpected, necessary and sufficient condition for the Newton–Okounkov body to be reflexive.
Similar Articles
  • Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2020): 17B10, 14L35, 14M25, 52B20
  • Retrieve articles in all journals with MSC (2020): 17B10, 14L35, 14M25, 52B20
Bibliographic Information
  • Christian Steinert
  • Affiliation: Department of Mathematics, Chair for Algebra and Representation Theory, RWTH Aachen University, 25042 Aachen, Germany
  • MR Author ID: 1492490
  • ORCID: 0000-0002-5947-7298
  • Email:
  • Received by editor(s): February 20, 2022
  • Received by editor(s) in revised form: May 12, 2022
  • Published electronically: August 16, 2022
  • © Copyright 2022 American Mathematical Society
  • Journal: Represent. Theory 26 (2022), 859-873
  • MSC (2020): Primary 17B10; Secondary 14L35, 14M25, 52B20
  • DOI:
  • MathSciNet review: 4469220