| | | |

## NON-CANCELLABLE ELEMENTS IN TYPE AFFINE C COXETER GROUPS

#### Dana C. Ernst [1]

##### 63 185

Let (W, S) be a Coxeter system and suppose that w ∈ W is fully commutative (in the sense of Stembridge) and has a reduced expression beginning (respectively, ending) with s ∈ S. If there exists t ∈ S such that s and t do not commute and tw (respectively, wt) is no longer fully commutative, we say that w is left (respectively, right) weak star reducible by s with respect to t. We say that a fully commutative element is non-cancellable if it is irreducible under weak star reductions. In this paper, we classify the noncancellable elements in Coxeter groups of types B and affine C. In a sequel to this paper, the classification of the non-cancellable elements play a pivotal role in inductive arguments used to prove the faithfulness of a diagrammatic representation of a generalized Temperley–Lieb algebra of type affine C.
Coxeter groups, non-cancellable, star operations, heaps
Other ID JA28ES95EU Articles Author: Dana C. Ernst
 Bibtex @ { ieja266440, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Abdullah HARMANCI}, year = {2010}, volume = {8}, pages = {191 - 218}, doi = {}, title = {NON-CANCELLABLE ELEMENTS IN TYPE AFFINE C COXETER GROUPS}, key = {cite}, author = {Ernst, Dana C.} } APA Ernst, D . (2010). NON-CANCELLABLE ELEMENTS IN TYPE AFFINE C COXETER GROUPS. International Electronic Journal of Algebra, 8 (8), 191-218. Retrieved from http://dergipark.org.tr/ieja/issue/25212/266440 MLA Ernst, D . "NON-CANCELLABLE ELEMENTS IN TYPE AFFINE C COXETER GROUPS". International Electronic Journal of Algebra 8 (2010): 191-218 Chicago Ernst, D . "NON-CANCELLABLE ELEMENTS IN TYPE AFFINE C COXETER GROUPS". International Electronic Journal of Algebra 8 (2010): 191-218 RIS TY - JOUR T1 - NON-CANCELLABLE ELEMENTS IN TYPE AFFINE C COXETER GROUPS AU - Dana C. Ernst Y1 - 2010 PY - 2010 N1 - DO - T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 191 EP - 218 VL - 8 IS - 8 SN - 1306-6048-1306-6048 M3 - UR - Y2 - 2019 ER - EndNote %0 International Electronic Journal of Algebra NON-CANCELLABLE ELEMENTS IN TYPE AFFINE C COXETER GROUPS %A Dana C. Ernst %T NON-CANCELLABLE ELEMENTS IN TYPE AFFINE C COXETER GROUPS %D 2010 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 8 %N 8 %R %U ISNAD Ernst, Dana C. . "NON-CANCELLABLE ELEMENTS IN TYPE AFFINE C COXETER GROUPS". International Electronic Journal of Algebra 8 / 8 (December 2010): 191-218.