Determination of the Characteristic Class Functions of the Weyl Group of type G2

Hasan Arslan

doi:10.29002/asujse.1207235

Research Article

Year 2023, , 1 - 5, 30.06.2023

Hasan Arslan

https://doi.org/10.29002/asujse.1207235

Abstract

References

[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).

Determination of the Characteristic Class Functions of the Weyl Group of type G2

Year 2023, , 1 - 5, 30.06.2023

Hasan Arslan

https://doi.org/10.29002/asujse.1207235

Abstract

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.

Keywords

Weyl group, descent algebra, generalized descent algebra, characteristic class function.

References

[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).

There are 7 citations in total.

Details

Primary Language	English
Journal Section	Research Article
Authors	Hasan Arslan 0000-0002-0430-8737
Publication Date	June 30, 2023
Submission Date	November 20, 2022
Acceptance Date	December 7, 2022
Published in Issue	Year 2023

Cite

APA	Arslan, H. (2023). Determination of the Characteristic Class Functions of the Weyl Group of type G2. Aksaray University Journal of Science and Engineering, 7(1), 1-5. https://doi.org/10.29002/asujse.1207235