Involutions in Weyl group of type F4

doi:10.1007/s11464-017-0646-z

Frontiers of Mathematics in China

2017, Vol. 12

Issue (4): 891-906 https://doi.org/10.1007/s11464-017-0646-z

本期目录

Involutions in Weyl group of type F4

Jun HU(

), Jing ZHANG, Yabo WU

School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China

全文: PDF(317 KB)

Abstract：

Let W be the Weyl group of type F₄: We explicitly describe a nite set of basic braid I_*-transformations and show that any two reduced I_*-expressions for a given involution in W can be transformed into each other through a series of basic braid I_*-transformations. Our main result extends the earlier work on the Weyl groups of classical types (i.e., A_n; B_n; and D_n).

Key words： Involutions reduced I_*-expressions braid I_*-transformations

收稿日期: 2016-09-28 出版日期: 2017-07-06

Corresponding Author(s): Jun HU

引用本文:

. [J]. Frontiers of Mathematics in China, 2017, 12(4): 891-906.
Jun HU, Jing ZHANG, Yabo WU. Involutions in Weyl group of type F4. Front. Math. China, 2017, 12(4): 891-906.

链接本文:

https://academic.hep.com.cn/fmc/CN/10.1007/s11464-017-0646-z
https://academic.hep.com.cn/fmc/CN/Y2017/V12/I4/891

1	CanM B, JoyceM, WyserB. Chains in weak order posets associated to involutions. J Combin Theory Ser A, 2016, 137: 207–225 https://doi.org/10.1016/j.jcta.2015.09.001
2	GeckM, PfeierG. Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras. London Math Soc Monogr New Ser, Vol 446. Oxford: Clarendon Press, 2000
3	HamakerZ, MarbergE, PawlowskiB. Involution words: counting problems and connections to Schubert calculus for symmetric orbit closures. arXiv: 1508.01823
4	HamakerZ, MarbergE, PawlowskiB. Involution words II: braid relations and atomic structures. J Algebraic Combin, 2017, 45: 701–743 https://doi.org/10.1007/s10801-016-0722-6
5	HultmanA. Fixed points of involutive automorphisms of the Bruhat order. Adv Math, 2005, 195(1): 283–296 https://doi.org/10.1016/j.aim.2004.08.011
6	HultmanA. The combinatorics of twisted involutions in Coxeter groups. Trans Amer Math Soc, 2007, 359(6): 2787–2798 https://doi.org/10.1090/S0002-9947-07-04070-6
7	HuJ, ZhangJ. On involutions in symmetric groups and a conjecture of Lusztig. Adv Math, 2016, 287: 1–30 https://doi.org/10.1016/j.aim.2015.10.003
8	HuJ, ZhangJ. On involutions in Weyl groups. J Lie Theory, 2017, 27: 671–706
9	LusztigG. A bar operator for involutions in a Coxeter groups. Bull Inst Math Acad Sin (NS), 2012, 7: 355–404
10	LusztigG. An involution based left ideal in the Hecke algebra. Represent Theory, 2016, 20(8): 172–186 https://doi.org/10.1090/ert/483
11	LusztigG, VoganD. Hecke algebras and involutions in Weyl groups. Bull Inst Math Acad Sin (NS), 2012, 7(3): 323–354
12	MarbergE. Braid relations for involution words in affine Coxeter groups. arXiv: 1703.10437
13	MatsumotoH. Générateurs et relations des groupes de Weyl généralisés. C R Acad Sci Paris, 1964, 258: 3419-3422
14	RichardsonR W, SpringerT A. The Bruhat on symmetric varieties. Geom Dedicata, 1990, 35: 389–436 https://doi.org/10.1007/BF00147354
15	RichardsonR W, SpringerT A. Complements to: The Bruhat on symmetric varieties. Geom Dedicata, 1994, 49: 231–238 https://doi.org/10.1007/BF01610623
16	WyserB J, YongA. Polynomials for symmetric orbit closures in the flag variety. Transform Groups, 2017, 22(1): 267–290 https://doi.org/10.1007/s00031-016-9381-x

Viewed

Full text

Abstract

Cited

Shared

Discussed