On dual canonical bases
Quantum Algebra
2009-11-11 v1 Representation Theory
Abstract
The dual basis of the canonical basis of the modified quantized enveloping algebra is studied, in particular for type . The construction of a basis for the coordinate algebra of the 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.
Cite
@article{arxiv.math/0510288,
title = {On dual canonical bases},
author = {Hechun Zhang},
journal= {arXiv preprint arXiv:math/0510288},
year = {2009}
}