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Gelfand–Zeitlin integrable system
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<p>In mathematics, the Gelfand–Zeitlin system (also written Gelfand–Zetlin system, Gelfand–Cetlin system, Gelfand–Tsetlin system) is an <a href="/facts/Integrable_system/Crgzjw6G">integrable system</a> on conjugacy classes of Hermitian matrices. It was introduced by Guillemin and Sternberg (1983), who named it after the <a href="/facts/Restricted_representation/rw7IN86T">Gelfand–Zeitlin basis</a>, an early example of <a href="/facts/Canonical_basis/I3dJq0Q3">canonical basis</a>, introduced by <a href="/facts/I._M._Gelfand/TJeJouKs">I. M. Gelfand</a> and <a href="/facts/M._L._Cetlin/Jms1sEJw">M. L. Cetlin</a> in 1950s. Kostant and Wallach (2006) introduced a complex version of this integrable system. </p> <ul><li>Guillemin, Victor; <a href="/facts/Shlomo_Sternberg/IsGM8VzY">Sternberg, Shlomo</a> (1983), "The Gel'fand-Cetlin system and quantization of the complex flag manifolds", <i>Journal of Functional Analysis</i>, 52 (1): 106–128, <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1016%2F0022-1236%2883%2990092-7">10.1016/0022-1236(83)90092-7</a>, <a href="/facts/ISSN_(identifier)/DPAflDvU">ISSN</a> <a href="https://search.worldcat.org/issn/0022-1236">0022-1236</a>, <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=0705993">0705993</a></li> <li><a href="/facts/Bertram_Kostant/TpckB9MH">Kostant, Bertram</a>; <a href="/facts/Nolan_Wallach/hpTW63TC">Wallach, Nolan</a> (2006), "Gelfand-Zeitlin theory from the perspective of classical mechanics. I", <i>Studies in Lie theory</i>, Progr. Math., vol. 243, Boston, MA: Birkhäuser Boston, pp. 319–364, <a href="/facts/ArXiv_(identifier)/H6EtgnBe">arXiv</a>:<a href="https://arxiv.org/abs/math/0408342">math/0408342</a>, <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2F0-8176-4478-4_12">10.1007/0-8176-4478-4_12</a>, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-8176-4342-3, <a href="/facts/MR_(identifier)/uP137L11">MR</a> <a href="https://mathscinet.ams.org/mathscinet-getitem?mr=2214253">2214253</a></li> <li>Kogan, Mikhail; Miller, Ezra (2005). <a href="https://doi.org/10.1016%2Fj.aim.2004.03.017">"Toric degeneration of Schubert varieties and Gelfand—Tsetlin polytopes"</a>. <i><a href="/facts/Advances_in_Mathematics/kXtcl4pM">Advances in Mathematics</a></i>. 193 (1): 1–17. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1016%2Fj.aim.2004.03.017">10.1016/j.aim.2004.03.017</a>.</li></ul>