Gelfand-Tsetlin basis

Gelʹfand-Cetlin or Gelfand-Tsetlin bases – an early example of canonical bases on the representations of Lie groups.

  • I. M. Gelʹfand, M. L. Cetlin, Finite-dimensional representations of the group of unimodular matrices, (Russian) Doklady Akad. Nauk SSSR (N.S.) 71, (1950) 825–828; Finite-dimensional representations of groups of orthogonal matrices, Doklady Akad. Nauk SSSR (N.S.) 71, (1950) 1017–1020.
  • Victor Guillemin, Shlomo Sternberg, The Gel’fand-Cetlin system and quantization of the complex flag manifolds, Journal of Functional Analysis 52 (1): 106–128, 1983 doi MR705993
  • D. P. Želobenko, Compact Lie groups and their representations
  • A. I. Molev, Gelfand-Tsetlin bases for classical Lie algebras, arxiv/0211289
  • Terry Tao, Gelfand obituary
  • Megumi Harada, The symplectic geometry of the Gel’fand-Cetlin-Molev basis for representations of Sp(2n,C), published pdf, math.SG/0404485
  • Grigori Olshanski, Projections of orbital measures, Gelfand-Tsetlin polytopes, and splines, arxiv/1302.7116
  • wikipedia Gelfand-Tsetlin integrable system
  • Bertram Kostant, Nolan Wallach, Gelfand-Zeitlin theory from the perspective of classical mechanics. I, Studies in Lie theory, Progr. Math. 243, Birkhäuser 2006, pp. 319–364

Created on March 1, 2013 at 21:23:34. See the history of this page for a list of all contributions to it.