Representations of $U_h(su(N))$ derived from quantum flag manifolds

Details Representations of $U_h(su(N))$ derived from quantum flag manifolds Representations of $U_h(su(N))$ derived from quantum flag manifolds

1996-10-24

arxiv.org/abs/q-alg/9610027v1

Mathematics

Quantum Algebra

LaTeX file, JMP (to appear)

Scientific paper

10.1063/1.531808

A relationship between quantum flag and Grassmann manifolds is revealed. This enables a formal diagonalization of quantum positive matrices. The requirement that this diagonalization defines a homomorphism leads to a left \Uh -- module structure on the algebra generated by quantum antiholomorphic coordinate functions living on the flag manifold. The module is defined by prescribing the action on the unit and then extending it to all polynomials using a quantum version of Leibniz rule. Leibniz rule is shown to be induced by the dressing transformation. For discrete values of parameters occuring in the diagonalization one can extract finite-dimensional irreducible representations of \Uh as cyclic submodules.

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