dorsal/arxiv
View SchemaRepresentations of $U_h(su(N))$ derived from quantum flag manifolds
| Authors | P. Stovicek, R. Twarock |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9610027 |
| URL | https://arxiv.org/abs/q-alg/9610027 |
| DOI | 10.1063/1.531808 |
Abstract
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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"abstract": "A relationship between quantum flag and Grassmann manifolds is revealed. This\nenables a formal diagonalization of quantum positive matrices. The requirement\nthat this diagonalization defines a homomorphism leads to a left \\Uh -- module\nstructure on the algebra generated by quantum antiholomorphic coordinate\nfunctions living on the flag manifold. The module is defined by prescribing the\naction on the unit and then extending it to all polynomials using a quantum\nversion of Leibniz rule. Leibniz rule is shown to be induced by the dressing\ntransformation. For discrete values of parameters occuring in the\ndiagonalization one can extract finite-dimensional irreducible representations\nof \\Uh as cyclic submodules.",
"arxiv_id": "q-alg/9610027",
"authors": [
"P. Stovicek",
"R. Twarock"
],
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],
"doi": "10.1063/1.531808",
"title": "Representations of $U_h(su(N))$ derived from quantum flag manifolds",
"url": "https://arxiv.org/abs/q-alg/9610027"
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