GelfandTsetlin polytopes and FeiginFourierLittelmann polytopes as marked poset polytopes
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 FeiginFourierLittelmann polytopes (2010), which arise in the representation 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 FeiginFourierLittelmann polytopes corresponding to the symplectic and odd orthogonal Lie algebras.
 Publication:

arXiv eprints
 Pub Date:
 August 2010
 arXiv:
 arXiv:1008.2365
 Bibcode:
 2010arXiv1008.2365A
 Keywords:

 Mathematics  Combinatorics;
 Mathematics  Representation Theory
 EPrint:
 12 pages