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Dual Canonical Bases for the Quantum Special Linear Group and Invariant Subalgebras

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Abstract

A string basis is constructed for each subalgebra of invariants of the function algebra on the quantum special linear group. By analyzing the string basis for a particular subalgebra of invariants, we obtain a “canonical basis” for every finite dimensional irreducible \(U_q({\mathfrak{sl}}(n))\)-module. It is also shown that the algebra of functions on any quantum homogeneous space is generated by quantum minors.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, P.R. China

    Hechun Zhang

  2. School of Mathematics and Statistics, University of Sydney, 1001, Sydney, Australia

    R. B. Zhang

Authors
  1. Hechun Zhang
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  2. R. B. Zhang
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Correspondence to R. B. Zhang.

Additional information

Supported by the Australian Research Council and Chinese National Natural Science Foundation project number: 10471070

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Zhang, H., Zhang, R.B. Dual Canonical Bases for the Quantum Special Linear Group and Invariant Subalgebras. Lett Math Phys 73, 165–181 (2005). https://doi.org/10.1007/s11005-005-0015-9

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  • DOI: https://doi.org/10.1007/s11005-005-0015-9

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