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

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

2005-09-28

arxiv.org/abs/math/0509651v1

Mathematics

Quantum Algebra

15 pages

Scientific paper

10.1007/s11005-005-0015-9

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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