V. A. Kirichenko, E. Yu. Smirnov, V. A. Timorin, “Schubert calculus and Gelfand–Zetlin polytopes”, Uspekhi Mat. Nauk, 2012, Volume 67, Issue 4(406),Pages <nobr>89

This article is cited in 28 papers

Schubert calculus and Gelfand–Zetlin polytopes

V. A. Kirichenko^ab, E. Yu. Smirnov^cb, V. A. Timorin^db

^a Institute for Information Transmission Problems of the Russian Academy of Sciences, Moscow, Russia
^b National Research University Higher School of Economics
^c Laboratoire J.-V. Poncelet (UMI 2615 du CNRS)
^d Independent University of Moscow

Abstract: A new approach is described to the Schubert calculus on complete flag varieties, using the volume polynomial associated with Gelfand–Zetlin polytopes. This approach makes it possible to compute the intersection products of Schubert cycles by intersecting faces of a polytope.
Bibliography: 23 titles.

Keywords: Flag variety, Schubert calculus, Gelfand–Zetlin polytope, volume polynomial.

UDC: 512.734

MSC: Primary 14L30; Secondary 52B20, 14M15, 14N15

Received: 25.05.2012

DOI: 10.4213/rm9492