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FFLV polytopes are string polytopes

Ester Cleusters, Ghislain Fourier, Felix Lerner

Abstract

In this paper, we establish that FFLV polytopes, which describe monomial bases compatible with the PBW filtration on finite-dimensional simple modules for $\lie{sl}_n$ and $\lie{sp}_n$, are actually string polytopes as described by Littelmann and Berenstein-Zelevinsky for Demazure modules of higher-rank Lie algebras.

FFLV polytopes are string polytopes

Abstract

In this paper, we establish that FFLV polytopes, which describe monomial bases compatible with the PBW filtration on finite-dimensional simple modules for and , are actually string polytopes as described by Littelmann and Berenstein-Zelevinsky for Demazure modules of higher-rank Lie algebras.
Paper Structure (9 sections, 11 theorems, 69 equations)

This paper contains 9 sections, 11 theorems, 69 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notations
  4. Monomial bases
  5. Degenerations
  6. Main theorem
  7. General setup
  8. Type A
  9. Type C

Key Result

Theorem 1.1

The FFLV polytope $FFLV(\lambda)$ is unimodularly equivalent to the string polytope $Q_{\underline{w}}(\tilde{\lambda})$.

Theorems & Definitions (33)

  • Theorem 1.1
  • Theorem 1.2
  • Proposition 2.3: FFL17
  • Remark 2.4
  • Theorem 3.1
  • Corollary 3.2
  • Remark 3.3
  • proof
  • Corollary 3.4
  • Definition 4.1
  • ...and 23 more