# The Canonical Basis of $\dot{\mathbf{U}}$ for Type $A_{2}$

• Published in 2012
The modified quantized enveloping algebra has a remarkable basis, called the canonical basis, which was introduced by Lusztig. In this paper, all these monomial elements of the canonical basis for type $A_{2}$ are determined and we also give a conjecture about all polynomial elements of the canonical basis.

## Other information

arxivId
1208.5531
keywords
algebra,canonical basis,the modified quantized enveloping,the quasi-

### BibTeX entry

@article{Cui2012,
abstract = {The modified quantized enveloping algebra has a remarkable basis, called the canonical basis, which was introduced by Lusztig. In this paper, all these monomial elements of the canonical basis for type {\$}A{\_}{\{}2{\}}{\$} are determined and we also give a conjecture about all polynomial elements of the canonical basis.},
archivePrefix = {arXiv},
arxivId = {1208.5531},
author = {Cui, Weideng},
eprint = {1208.5531},
keywords = {algebra,canonical basis,the modified quantized enveloping,the quasi-},
month = {aug},
title = {The Canonical Basis of {\$}\dot{\{}\mathbf{\{}U{\}}{\}}{\$} for Type {\$}A{\_}{\{}2{\}}{\$}},
url = {http://arxiv.org/abs/1208.5531 http://arxiv.org/pdf/1208.5531v3},
year = 2012,
primaryClass = {math.RT},
urldate = {2012-08-29}
}