FFLV polytopes for odd symplectic Lie algebras

2021/10/01 by Rybin, Dmitry
#05E10 #17B10 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2110.00608

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.

Related

• FFLV polytopes are string polytopes
• Vertices of FFLV polytopes
• Polytope sums and Lie characters
• Strongly Homotopy Lie Algebras of One Even and Two Odd Dimensions
• Deformations of graded Lie algebras and symplectic structures