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

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