In mathematics, the Gelfand–Zeitlin system (also written Gelfand–Zetlin system, Gelfand–Cetlin system, Gelfand–Tsetlin system) is an integrable system on conjugacy classes of Hermitian matrices. It was introduced by Guillemin and Sternberg (1983), who named it after the Gelfand–Zeitlin basis, an early example of canonical basis, introduced by I. M. Gelfand and M. L. Cetlin in 1950s. Kostant and Wallach (2006) introduced a complex version of this integrable system.
Referencesedit
Guillemin, Victor; Sternberg, Shlomo (1983), "The Gel'fand-Cetlin system and quantization of the complex flag manifolds", Journal of Functional Analysis, 52 (1): 106–128, doi:10.1016/0022-1236(83)90092-7, ISSN 0022-1236, MR 0705993
Kostant, Bertram; Wallach, Nolan (2006), "Gelfand-Zeitlin theory from the perspective of classical mechanics. I", Studies in Lie theory, Progr. Math., vol. 243, Boston, MA: Birkhäuser Boston, pp. 319–364, arXiv:math/0408342, doi:10.1007/0-8176-4478-4_12, ISBN978-0-8176-4342-3, MR 2214253
Kogan, Mikhail; Miller, Ezra (2005). "Toric degeneration of Schubert varieties and Gelfand—Tsetlin polytopes". Advances in Mathematics. 193 (1): 1–17. doi:10.1016/j.aim.2004.03.017.
gelfand, zeitlin, integrable, system, mathematics, gelfand, zeitlin, system, also, written, gelfand, zetlin, system, gelfand, cetlin, system, gelfand, tsetlin, system, integrable, system, conjugacy, classes, hermitian, matrices, introduced, guillemin, sternber. In mathematics the Gelfand Zeitlin system also written Gelfand Zetlin system Gelfand Cetlin system Gelfand Tsetlin system is an integrable system on conjugacy classes of Hermitian matrices It was introduced by Guillemin and Sternberg 1983 who named it after the Gelfand Zeitlin basis an early example of canonical basis introduced by I M Gelfand and M L Cetlin in 1950s Kostant and Wallach 2006 introduced a complex version of this integrable system References editGuillemin Victor Sternberg Shlomo 1983 The Gel fand Cetlin system and quantization of the complex flag manifolds Journal of Functional Analysis 52 1 106 128 doi 10 1016 0022 1236 83 90092 7 ISSN 0022 1236 MR 0705993 Kostant Bertram Wallach Nolan 2006 Gelfand Zeitlin theory from the perspective of classical mechanics I Studies in Lie theory Progr Math vol 243 Boston MA Birkhauser Boston pp 319 364 arXiv math 0408342 doi 10 1007 0 8176 4478 4 12 ISBN 978 0 8176 4342 3 MR 2214253 Kogan Mikhail Miller Ezra 2005 Toric degeneration of Schubert varieties and Gelfand Tsetlin polytopes Advances in Mathematics 193 1 1 17 doi 10 1016 j aim 2004 03 017 External links edithttp ncatlab org nlab show Gelfand Tsetlin basis Retrieved from https en wikipedia org w index php title Gelfand Zeitlin integrable system amp oldid 1194582462, wikipedia, wiki, book, books, library,
