nLab
Gelfand-Tsetlin basis

Contents

Context

Algebra

Representation theory

Contents

Idea

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

References

Original articles:

  • Israel Gelfand, 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.

Review:

See also:

  • 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

Last revised on May 19, 2021 at 09:44:18. See the history of this page for a list of all contributions to it.