Communications in Mathematical Physics

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

Quantum Grassmann manifolds

  • P. Šťovíček


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.


Neural Network Manifold Statistical Physic Complex System Nonlinear Dynamics 
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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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