FFLV polytopes for odd symplectic Lie algebras

TL;DR

This paper introduces FFLV polytopes for odd symplectic Lie algebras, providing new combinatorial models and character formulas for their representations.

Contribution

It constructs FFLV polytopes for odd symplectic Lie algebras and establishes their properties, including graded character formulas and PBW bases.

Findings

Established FFLV polytopes for odd symplectic Lie algebras

Derived a new graded character formula

Constructed PBW bases for these algebras

Abstract

We consider "odd symplectic Lie algebras" defined in terms of maximal rank skew-symmetric forms. We provide FFLV polytopes for these algebras and prove their standard properties. In particular, we obtain a new graded character formula and PBW bases for an analogue of irreducible representations in terms of lattice points of FFLV polytopes.