On dual canonical bases

Details On dual canonical bases On dual canonical bases

2005-10-13

arxiv.org/abs/math/0510288v1

J. Phys. A 37 (2004), no. 32, 7879--7893

Mathematics

Quantum Algebra

Scientific paper

10.1088/0305-4470/37/32/004

The dual basis of the canonical basis of the modified quantized enveloping algebra is studied, in particular for type $A$. The construction of a basis for the coordinate algebra of the $n\times n$ quantum matrices is appropriate for the study the multiplicative property. It is shown that this basis is invariant under multiplication by certain quantum minors including the quantum determinant. Then a basis of quantum SL(n) is obtained by setting the quantum determinant to one. This basis turns out to be equivalent to the dual canonical basis.

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