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Russian Mathematical Surveys, 2012, Volume 67, Issue 4, Pages 685–719
DOI: https://doi.org/10.1070/RM2012v067n04ABEH004804 (Mi rm9492) 		 
This article is cited in 28 scientific papers (total in 28 papers)

Schubert calculus and Gelfand–Zetlin polytopes

V. A. Kirichenkoab, E. Yu. Smirnovcb, V. A. Timorindb

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
English version PDF (777 kB) Citations (28)
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DOI: https://doi.org/10.1070/RM2012v067n04ABEH004804
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.
Received: 25.05.2012
Russian version:
Uspekhi Matematicheskikh Nauk, 2012, Volume 67, Issue 4(406), Pages 89–128
DOI: https://doi.org/10.4213/rm9492
Bibliographic databases:
Document Type: Article
UDC: 512.734
MSC: Primary 14L30; Secondary 52B20, 14M15, 14N15
Language: English
Original paper language: Russian
Citation: V. A. Kirichenko, E. Yu. Smirnov, V. A. Timorin, “Schubert calculus and Gelfand–Zetlin polytopes”, Uspekhi Mat. Nauk, 67:4(406) (2012), 89–128; Russian Math. Surveys, 67:4 (2012), 685–719
Citation in format AMSBIB
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