Hook removal operators on the odd Young graph

Bessenrodt, Christine; Giannelli, Eugenio; Olsson, Jørn B.

doi:10.5802/alco.42

Bessenrodt, Christine ¹ ; Giannelli, Eugenio ² ; Olsson, Jørn B.³

¹ Institute for Algebra, Number Theory and Discrete Mathematics, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
² Dipartimento di Matematica “U. Dini”, Université degli Studi di Firenze, Firenze, 50134 Italy
³ Department of Mathematical Sciences, University of Copenhagen, DK-2100 Copenhagen Ø, Denmark

Algebraic Combinatorics, Tome 2 (2019) no. 2, pp. 249-274.

Résumé

In this article we consider hook removal operators on odd partitions, i.e., partitions labelling odd-degree irreducible characters of finite symmetric groups. In particular we complete the discussion, started in [8] and developed in [3], concerning the commutativity of such operators.

Reçu le : 2017-11-24
Révisé le : 2018-07-23
Accepté le : 2018-08-30
Publié le : 2019-03-05

MR Zbl

DOI : 10.5802/alco.42

Classification : 20C15
Mots clés : Symmetric groups, Young graph

Affiliations des auteurs :

Bessenrodt, Christine ¹ ; Giannelli, Eugenio ² ; Olsson, Jørn B. ³

@article{ALCO_2019__2_2_249_0,
     author = {Bessenrodt, Christine and Giannelli, Eugenio and Olsson, J{\o}rn B.},
     title = {Hook removal operators on the odd {Young} graph},
     journal = {Algebraic Combinatorics},
     pages = {249--274},
     publisher = {MathOA foundation},
     volume = {2},
     number = {2},
     year = {2019},
     doi = {10.5802/alco.42},
     mrnumber = {3934830},
     zbl = {07049525},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/alco.42/}
}

TY  - JOUR
AU  - Bessenrodt, Christine
AU  - Giannelli, Eugenio
AU  - Olsson, Jørn B.
TI  - Hook removal operators on the odd Young graph
JO  - Algebraic Combinatorics
PY  - 2019
SP  - 249
EP  - 274
VL  - 2
IS  - 2
PB  - MathOA foundation
UR  - http://www.numdam.org/articles/10.5802/alco.42/
DO  - 10.5802/alco.42
LA  - en
ID  - ALCO_2019__2_2_249_0
ER  -

%0 Journal Article
%A Bessenrodt, Christine
%A Giannelli, Eugenio
%A Olsson, Jørn B.
%T Hook removal operators on the odd Young graph
%J Algebraic Combinatorics
%D 2019
%P 249-274
%V 2
%N 2
%I MathOA foundation
%U http://www.numdam.org/articles/10.5802/alco.42/
%R 10.5802/alco.42
%G en
%F ALCO_2019__2_2_249_0

Bessenrodt, Christine; Giannelli, Eugenio; Olsson, Jørn B. Hook removal operators on the odd Young graph. Algebraic Combinatorics, Tome 2 (2019) no. 2, pp. 249-274. doi : 10.5802/alco.42. http://www.numdam.org/articles/10.5802/alco.42/

Bibliographie
Cité par

[1] Ayyer, Arvind; Prasad, Amritanshu; Spallone, Steven Odd partitions in Young’s lattice, Sémin. Lothar. Comb., Volume 75 (2016), B75g, 13 pages | MR | Zbl

[2] Bessenrodt, Christine On hooks of Young diagrams, Ann. Comb., Volume 2 (1998) no. 2, pp. 103-110 | DOI | MR | Zbl

[3] Bessenrodt, Christine; Giannelli, Eugenio; Olsson, Jørn B. Restriction of odd degree characters of $𝔖_{n}$ , SIGMA, Symmetry Integrability Geom. Methods Appl., Volume 13 (2017), 070, 10 pages | DOI | MR | Zbl

[4] Feit, Walter Characters of finite groups, W. A. Benjamin, 1967, viii+186 pages | MR | Zbl

[5] Giannelli, Eugenio Characters of odd degree of symmetric groups, J. Lond. Math. Soc., Volume 96 (2017) no. 1, pp. 1-14 | DOI | MR | Zbl

[6] Giannelli, Eugenio; Kleshchev, Alexander; Navarro, Gabriel; Tiep, Pham Huu Restriction of odd degree characters and natural correspondences, Int. Math. Res. Not. (2017) no. 20, pp. 6089-6118 | DOI | MR | Zbl

[7] Giannelli, Eugenio; Law, Stacey; Martin, Stuart On the $p^{'}$ -subgraph of the Young graph (2018) (to appear in Algebr. Represent. Theory) | arXiv | Zbl

[8] Isaacs, I. Martin; Navarro, Gabriel; Olsson, Jørn B.; Tiep, Pham Huu Character restrictions and multiplicities in symmetric groups, J. Algebra, Volume 478 (2017), pp. 271-282 | DOI | MR | Zbl

[9] James, Gordon The representation theory of the symmetric groups, Lecture Notes in Mathematics, 682, Springer, 1978, v+156 pages | MR

[10] James, Gordon; Kerber, Adalbert The representation theory of the symmetric group, Encyclopedia of Mathematics and Its Applications, 16, Addison-Wesley Publishing Co., 1981, xxviii+510 pages (With a foreword by P. M. Cohn, With an introduction by Gilbert de B. Robinson) | MR | Zbl

[11] McKay, John Irreducible representations of odd degree, J. Algebra, Volume 20 (1972), pp. 416-418 | DOI | MR | Zbl

[12] Olsson, Jørn B. Combinatorics and Representations of finite groups, Vorlesungen aus dem Fachbereich Mathematik der Universität Essen, 20, Univ. GH Essen, 1994, 94 pages | Zbl

Cité par Sources :