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Communications in Mathematical Physics

, Volume 158, Issue 1, pp 135–153 | Cite as

Quantum Grassmann manifolds

  • P. Šťovíček
Article

Abstract

Orbits of the quantum dressing transformation forSU q (N) acting on its solvable dual are introduced. The case is considered when the corresponding classical orbits coincide with Grassmann manifolds. Quantization of the Poisson bracket on a Zariski open subset of the Grassmann manifold yields a *-algebra generated by the quantum coordinate functions. The commutation relations are written in a compact form with the help of theR-matrix. Finite-dimensional irreducible representations ofU h \((\mathfrak{s}\mathfrak{l}(N,\mathbb{C}))\) are derived from the *-algebra structure.

Keywords

Neural Network Manifold Statistical Physic Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • P. Šťovíček
    • 1
  1. 1.Department of MathematicsFaculty of Nuclear Science, CTUPragueCzech Republic

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