Divided difference operators on polytopes
Valentina Kiritchenko
TL;DR
This paper introduces convex-geometric divided difference operators to construct polytopes representing Demazure characters, unifying Gelfand-Zetlin polytopes and Grossberg-Karshon twisted cubes.
Contribution
It defines new convex-geometric operators that systematically generate polytopes for Demazure characters, linking various known polytopes in a unified framework.
Findings
Constructed polytopes for Demazure characters using new operators
Unified Gelfand-Zetlin polytopes and twisted cubes within a single approach
Provided a systematic method for inductively building these polytopes
Abstract
We define convex-geometric counterparts of divided difference (or Demazure) operators from the Schubert calculus and representation theory. These operators are used to construct inductively polytopes that capture Demazure characters of representations of reductive groups. In particular, Gelfand-Zetlin polytopes and twisted cubes of Grossberg-Karshon are obtained in a uniform way.
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