Summary: Gelfand­Tsetlin Polytopes and
Feigin­Fourier­Littelmann­Vinberg Polytopes as
Marked Poset Polytopes
Federico Ardila
Thomas Bliem
Dido Salazar
Abstract
Stanley (1986) showed how a finite partially ordered set gives rise to two
polytopes, called the order polytope and chain polytope, which have the
same Ehrhart polynomial despite being quite different combinatorially.
We generalize his result to a wider family of polytopes constructed from a
poset P with integers assigned to some of its elements.
Through this construction, we explain combinatorially the relationship
between the Gelfand­Tsetlin polytopes (1950) and the Feigin­Fourier­
Littelmann­Vinberg polytopes (2010, 2005), which arise in the representa-
tion theory of the special linear Lie algebra. We then use the generalized
Gelfand­Tsetlin polytopes of Berenstein and Zelevinsky (1989) to propose
conjectural analogues of the Feigin­Fourier­Littelmann­Vinberg polytopes
corresponding to the symplectic and odd orthogonal Lie algebras.
1 Introduction

Source: Ardila, Federico - Department of Mathematics, San Francisco State University

Collections: Mathematics