TY - JOUR
T1 - The Face Structure and Geometry of Marked Order Polyhedra
AU - Pegel, Christoph
PY - 2018/11
Y1 - 2018/11
N2 - We study a class of polyhedra associated to marked posets. Examples of these polyhedra are Gelfand–Tsetlin polytopes and cones, as well as Berenstein–Zelevinsky polytopes—all of which have appeared in the representation theory of semi-simple Lie algebras. The faces of these polyhedra correspond to certain partitions of the underlying poset and we give a combinatorial characterization of these partitions. We specify a class of marked posets that give rise to polyhedra with facets in correspondence to the covering relations of the poset. On the convex geometrical side, we describe the recession cone of the polyhedra, discuss products and give a Minkowski sum decomposition. We briefly discuss intersections with affine subspaces that have also appeared in representation theory and recently in the theory of finite Hilbert space frames.
AB - We study a class of polyhedra associated to marked posets. Examples of these polyhedra are Gelfand–Tsetlin polytopes and cones, as well as Berenstein–Zelevinsky polytopes—all of which have appeared in the representation theory of semi-simple Lie algebras. The faces of these polyhedra correspond to certain partitions of the underlying poset and we give a combinatorial characterization of these partitions. We specify a class of marked posets that give rise to polyhedra with facets in correspondence to the covering relations of the poset. On the convex geometrical side, we describe the recession cone of the polyhedra, discuss products and give a Minkowski sum decomposition. We briefly discuss intersections with affine subspaces that have also appeared in representation theory and recently in the theory of finite Hilbert space frames.
KW - Gelfand–Tsetlin polytopes
KW - Marked poset polytopes
KW - Polyhedral geometry
KW - Representation theory
UR - http://www.scopus.com/inward/record.url?scp=85035132784&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1610.01393
DO - 10.48550/arXiv.1610.01393
M3 - Article
VL - 35
SP - 467
EP - 488
JO - Order
JF - Order
SN - 0167-8094
IS - 3
ER -