Vertices of Gelfand-Tsetlin Polytopes
| dc.creator | De Loera, Jesús A. | |
| dc.creator | McAllister, Tyrrell B. | |
| dc.date | 2003-09-19 | |
| dc.date | 2003-09-23 | |
| dc.date.accessioned | 2026-07-07T05:01:18Z | |
| dc.date.available | 2026-07-07T05:01:18Z | |
| dc.description | This paper is a study of the polyhedral geometry of Gelfand-Tsetlin patterns arising in the representation theory $\mathfrak{gl}_n \C$ and algebraic combinatorics. We present a combinatorial characterization of the vertices and a method to calculate the dimension of the lowest-dimensional face containing a given Gelfand-Tsetlin pattern. As an application, we disprove a conjecture of Berenstein and Kirillov about the integrality of all vertices of the Gelfand-Tsetlin polytopes. We can construct for each $n\geq5$ a counterexample, with arbitrarily increasing denominators as $n$ grows, of a non-integral vertex. This is the first infinite family of non-integral polyhedra for which the Ehrhart counting function is still a polynomial. We also derive a bound on the denominators for the non-integral vertices when $n$ is fixed. | |
| dc.description | 14 pages, 3 figures, fixed attributions | |
| dc.identifier | https://arxiv.org/abs/math/0309329 | |
| dc.identifier | http://arxiv.org/abs/math/0309329 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68624 | |
| dc.subject | Combinatorics | |
| dc.subject | Representation Theory | |
| dc.title | Vertices of Gelfand-Tsetlin Polytopes | |
| dc.type | text |