Öz
Kaynakça
- [1] V. Reiner, Descents and one-dimensional characters for classical Weyl groups, Discrete Math. 140 (1995) 129-140. DOI: https://doi.org/10.1016/0012-365X(93)E0179-8
- [2] J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge Studies in Advenced Math., vol. 29, Cambridge University Press. (1990).
- [3] R. Mantaci, C. Reutenauer, A generalization of Solomon’s algebra for hyperoctahedral groups and other wreath products, Comm. in Algebra. 23(1) (1995) 27–56. DOI: https://doi.org/10.1080/00927879508825205
- [4] H. Arslan, H. Can, (2020). Generalized Burnside algebra of type . Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 69(1), 252-265. DOI: https://doi.org/10.31801/cfsuasmas.599246
- [5] C. Hohlweg, (2007). Generalized Descent Algebras. Canadian Mathematical Bulletin, 50(4), 535-546. DOI: https://doi.org/10.4153/CMB-2007-052-4
- [6] L. Solomon, A Mackey formula in the group ring of a Coxeter group, J. Algebra. 41(2) (1976) 255-264. DOI: https://doi.org/10.1016/0021-8693(76)90182-4
- [7] G. James, M. Liebeck, Representations and Characters of Groups, Cambridge: Cambridge University Press. (2001).
Öz
In this paper, our main objective is to combinatorially obtain all characteristic class functions of the Weyl group of type G2 with the help of the structure of generalized descent algebra including Solomon’s descent algebra and Mantaci-Reutenauer algebra. We also give an interpretation of the character table of the Weyl group of type G2 in terms of the permutation characters defined on the set of cosets belonging to each of its some special subgroups.
Anahtar Kelimeler
Weyl group descent algebra generalized descent algebra characteristic class function.
Kaynakça
- [1] V. Reiner, Descents and one-dimensional characters for classical Weyl groups, Discrete Math. 140 (1995) 129-140. DOI: https://doi.org/10.1016/0012-365X(93)E0179-8
- [2] J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge Studies in Advenced Math., vol. 29, Cambridge University Press. (1990).
- [3] R. Mantaci, C. Reutenauer, A generalization of Solomon’s algebra for hyperoctahedral groups and other wreath products, Comm. in Algebra. 23(1) (1995) 27–56. DOI: https://doi.org/10.1080/00927879508825205
- [4] H. Arslan, H. Can, (2020). Generalized Burnside algebra of type . Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 69(1), 252-265. DOI: https://doi.org/10.31801/cfsuasmas.599246
- [5] C. Hohlweg, (2007). Generalized Descent Algebras. Canadian Mathematical Bulletin, 50(4), 535-546. DOI: https://doi.org/10.4153/CMB-2007-052-4
- [6] L. Solomon, A Mackey formula in the group ring of a Coxeter group, J. Algebra. 41(2) (1976) 255-264. DOI: https://doi.org/10.1016/0021-8693(76)90182-4
- [7] G. James, M. Liebeck, Representations and Characters of Groups, Cambridge: Cambridge University Press. (2001).
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Haziran 2023 |
| Gönderilme Tarihi | 20 Kasım 2022 |
| Kabul Tarihi | 7 Aralık 2022 |
| Yayımlandığı Sayı | Yıl 2023Cilt: 7 Sayı: 1 |
