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Dual canonical bases for the quantum special linear group and invariant subalgebras

Hechun Zhang·R. B. Zhang
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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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Hechun Zhang, R. B. Zhang. 2005-09-28. Dual canonical bases for the quantum special linear group and invariant subalgebras. https://doi.org/10.1007/s11005-005-0015-9

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