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

• Published in 2012
• Added on 2012-08-29

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.

Links

• http://arxiv.org/abs/1208.5531
• http://arxiv.org/pdf/1208.5531v3

Other information

BibTeX entry

@article{Cui2012,
	key = {Cui2012},
	type = {article},
	title = {The Canonical Basis of {\$}\dot{\{}\mathbf{\{}U{\}}{\}}{\$} for Type {\$}A{\_}{\{}2{\}}{\$}},
	author = {Cui, Weideng},
	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.},
	comment = {},
	date_added = {2012-08-29},
	date_published = {2012-08-01},
	urls = {http://arxiv.org/abs/1208.5531,http://arxiv.org/pdf/1208.5531v3},
	collections = {},
	archivePrefix = {arXiv},
	arxivId = {1208.5531},
	eprint = {1208.5531},
	keywords = {algebra,canonical basis,the modified quantized enveloping,the quasi-},
	month = {aug},
	url = {http://arxiv.org/abs/1208.5531 http://arxiv.org/pdf/1208.5531v3},
	year = 2012,
	primaryClass = {math.RT},
	urldate = {2012-08-29}
}