Comptes Rendus
Combinatorics, Group theory
Affine twisted length function
Comptes Rendus. Mathématique, Volume 359 (2021) no. 7, pp. 873-879.

Let W a be an affine Weyl group. In 1987 Jian Yi Shi gave a characterization of the elements wW a in terms of Φ + -tuples (k(w,α)) αΦ + called the Shi vectors. Using these coefficients, a formula is provided to compute the standard length of W a . In this note we express the twisted affine length function of W a in terms of the Shi coefficients.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/crmath.227

Nathan Chapelier-Laget 1

1 Institut Denis Poisson at the University of Tours (CNRS), France.
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
@article{CRMATH_2021__359_7_873_0,
     author = {Nathan Chapelier-Laget},
     title = {Affine twisted length function},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {873--879},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {359},
     number = {7},
     year = {2021},
     doi = {10.5802/crmath.227},
     zbl = {07398740},
     language = {en},
}
TY  - JOUR
AU  - Nathan Chapelier-Laget
TI  - Affine twisted length function
JO  - Comptes Rendus. Mathématique
PY  - 2021
SP  - 873
EP  - 879
VL  - 359
IS  - 7
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.227
LA  - en
ID  - CRMATH_2021__359_7_873_0
ER  - 
%0 Journal Article
%A Nathan Chapelier-Laget
%T Affine twisted length function
%J Comptes Rendus. Mathématique
%D 2021
%P 873-879
%V 359
%N 7
%I Académie des sciences, Paris
%R 10.5802/crmath.227
%G en
%F CRMATH_2021__359_7_873_0
Nathan Chapelier-Laget. Affine twisted length function. Comptes Rendus. Mathématique, Volume 359 (2021) no. 7, pp. 873-879. doi : 10.5802/crmath.227. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.227/

[1] Matthew Dyer Hecke algebras and shellings of Bruhat intervals II; twisted Bruhat orders, Kazhdan–Lusztig theory and related topics. Proceedings of an AMS special session, held May 19-20, 1989 at the University of Chicago, Lake Shore Campus, Chicago, IL, USA (Contemporary Mathematics), Volume 139, American Mathematical Society, 1992, pp. 141-165 | MR | Zbl

[2] Matthew Dyer Hecke algebras and shellings of Bruhat intervals, Compos. Math., Volume 89 (1993) no. 1, pp. 91-115 | Numdam | MR | Zbl

[3] Matthew Dyer Reflection orders of affine Weyl groups (2014) (preprint)

[4] Matthew Dyer On the weak order of Coxeter groups, Can. J. Math., Volume 71 (2019) no. 2, pp. 299-336 | DOI | MR | Zbl

[5] Matthew Dyer; Christophe Hohlweg Small roots, low elements, and the weak order in Coxeter groups, Adv. Math., Volume 301 (2016), pp. 739-784 | DOI | MR | Zbl

[6] Matthew Dyer; Gus Lehrer Reflection subgroups of finite and affine Weyl groups, Trans. Am. Math. Soc., Volume 363 (2011) no. 11, pp. 5971-6005 | DOI | MR | Zbl

[7] Tom Edgar Sets of reflections defining twisted Bruhat orders, J. Algebr. Comb., Volume 26 (2007) no. 3, pp. 357-362 | DOI | MR | Zbl

[8] Christophe Hohlweg; Jean-Christophe Labbé On inversion sets and the weak order in Coxeter groups, Eur. J. Comb., Volume 55 (2016), pp. 1-19 | DOI | MR | Zbl

[9] James E. Humphreys Reflection groups and Coxeter groups, Cambridge Studies in Advanced Mathematics, 29, Cambridge University Press, 1990 | MR | Zbl

[10] George Lusztig Hecke algebras and Jantzen’s generic decomposition patterns, Adv. Math., Volume 37 (1980) no. 2, pp. 121-164 | DOI | MR | Zbl

[11] Weijia Wang Reduced expression of minimal infinite reduced words of affine Weyl groups (2020) (https://arxiv.org/abs/2001.09848)

[12] Jian Yi Shi Alcoves corresponding to an affine Weyl group, J. Lond. Math. Soc., Volume 35 (1987) no. 1, pp. 42-55 | MR | Zbl

Cited by Sources:

Comments - Policy