Almost all wreath product character values are divisible by given primes
Algebraic Combinatorics, Volume 6 (2023) no. 6, pp. 1519-1531.

For a finite group G with integer-valued character table and a prime p, we show that almost every entry in the character table of GS N is divisible by p as N. This result generalizes the work of Peluse and Soundararajan on the character table of S N .

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.313
Classification: 20C15, 05E10

Dong, Brandon 1; Graff, Hannah 2; Mundinger, Joshua 3; Rothstein, Skye 4; Vescovo, Lola 5

1 Carnegie Mellon University Pittsburgh PA
2 Creighton University Omaha NE
3 University of Chicago Chicago IL
4 Bard College Annandale-on-Hudson NY
5 Macalester College Saint Paul MN
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
@article{ALCO_2023__6_6_1519_0,
     author = {Dong, Brandon and Graff, Hannah and Mundinger, Joshua and Rothstein, Skye and Vescovo, Lola},
     title = {Almost all wreath product character values are divisible by given primes},
     journal = {Algebraic Combinatorics},
     pages = {1519--1531},
     publisher = {The Combinatorics Consortium},
     volume = {6},
     number = {6},
     year = {2023},
     doi = {10.5802/alco.313},
     language = {en},
     url = {https://alco.centre-mersenne.org/articles/10.5802/alco.313/}
}
TY  - JOUR
AU  - Dong, Brandon
AU  - Graff, Hannah
AU  - Mundinger, Joshua
AU  - Rothstein, Skye
AU  - Vescovo, Lola
TI  - Almost all wreath product character values are divisible by given primes
JO  - Algebraic Combinatorics
PY  - 2023
SP  - 1519
EP  - 1531
VL  - 6
IS  - 6
PB  - The Combinatorics Consortium
UR  - https://alco.centre-mersenne.org/articles/10.5802/alco.313/
DO  - 10.5802/alco.313
LA  - en
ID  - ALCO_2023__6_6_1519_0
ER  - 
%0 Journal Article
%A Dong, Brandon
%A Graff, Hannah
%A Mundinger, Joshua
%A Rothstein, Skye
%A Vescovo, Lola
%T Almost all wreath product character values are divisible by given primes
%J Algebraic Combinatorics
%D 2023
%P 1519-1531
%V 6
%N 6
%I The Combinatorics Consortium
%U https://alco.centre-mersenne.org/articles/10.5802/alco.313/
%R 10.5802/alco.313
%G en
%F ALCO_2023__6_6_1519_0
Dong, Brandon; Graff, Hannah; Mundinger, Joshua; Rothstein, Skye; Vescovo, Lola. Almost all wreath product character values are divisible by given primes. Algebraic Combinatorics, Volume 6 (2023) no. 6, pp. 1519-1531. doi : 10.5802/alco.313. https://alco.centre-mersenne.org/articles/10.5802/alco.313/

[1] Frobenius, Georg Ferdinand Über die Charaktere der symmetrischen Gruppe, Sitzungsberichte der Königliche Akademie der Wissenschaften (1900), pp. 516-534 | Zbl

[2] Geck, Meinolf; Pfeiffer, Götz Characters of finite Coxeter groups and Iwahori-Hecke algebras, London Mathematical Society Monographs, New Series, Oxford University Press, 2000 no. 21 | DOI

[3] Hardy, G. H.; Ramanujan, S. Asymptotic Formulæ in Combinatory Analysis, Proc. London Math. Soc. (2), Volume 17 (1918), pp. 75-115 | DOI | Zbl

[4] James, G.; Kerber, A. The representation theory of the symmetric group, Encyclopedia of Mathematics and its Applications, Addison-Wesley, 1981 no. 16

[5] Macdonald, Ian Grant Symmetric functions and Hall polynomials, Oxford Mathematical Monographs, Oxford University Press, 1995 | DOI

[6] Miller, Alexander R. Congruences in character tables of symmetric groups, 2019 | arXiv | DOI

[7] Miller, Alexander R. On parity and characters of symmetric groups, J. Combin. Theory Ser. A, Volume 162 (2019), pp. 231-240 | DOI | MR | Zbl

[8] Peluse, Sarah; Soundararajan, Kannan Almost all entries in the character table of the symmetric group are multiples of any given prime, J. Reine Angew. Math., Volume 786 (2022), pp. 45-53 | DOI | MR | Zbl

[9] Ram Murty, M. The partition function revisited, The legacy of Srinivasa Ramanujan (Lect. Notes Ser.), Volume 20, Ramanujan Math. Soc. (2013), pp. 261-279 | MR | Zbl

[10] Serre, Jean-Pierre Linear representations of finite groups, Graduate Texts in Mathematics, Vol. 42, Springer-Verlag, 1977 | DOI

[11] Specht, Wilhelm Eine Verallgemeinerung der symmetrischen Gruppe, Ph. D. Thesis, Humboldt-Universität zu Berlin (1932)

[12] Young, Alfred On quantitative substitutional analysis (fifth paper), Proc. London Math. Soc. (2), Volume 31 (1930) no. 4, pp. 273-288 | DOI | MR | Zbl

[13] Zelevinsky, Andrey V. Representations of finite classical groups. A Hopf algebra approach, Lecture Notes in Mathematics, 869, Springer-Verlag, 1981 | MR

Cited by Sources: