Geodesic
Properties of some character tables related to the symmetric groups
Journal of Algebraic Combinatorics, Tome 21 (2005) no. 2, pp. 163-177.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We determine invariants like the Smith normal form and the determinant for certain integral matrices which arise from the character tables of the symmetric groups $S _{ n}$ and their double covers. In particular, we give a simple computation, based on the theory of Hall-Littlewood symmetric functions, of the determinant of the regular character table $chi _{RC}$ of $S _{ n}$ with respect to an integer $rge$ 2. This result had earlier been proved by Olsson in a longer and more indirect manner. As a consequence, we obtain a new proof of the Mathas $rsquo$ Conjecture on the determinant of the Cartan matrix of the Iwahori-Hecke algebra. When $r$ is prime we determine the Smith normal form of $chi _{RC}$. Taking $r$ large yields the Smith normal form of the full character table of $S _{ n}$. Analogous results are then given for spin characters.
Keywords: keywords symmetric group, character, spin character, Smith normal form 
@article{JAC_2005__21_2_a2,
     author = {Bessenrodt, Christine and Olsson, J{\o}rn B. and Stanley, Richard P.},
     title = {Properties of some character tables related to the symmetric groups},
     journal = {Journal of Algebraic Combinatorics},
     pages = {163--177},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2005__21_2_a2/}
}
TY  - JOUR
AU  - Bessenrodt, Christine
AU  - Olsson, Jørn B.
AU  - Stanley, Richard P.
TI  - Properties of some character tables related to the symmetric groups
JO  - Journal of Algebraic Combinatorics
PY  - 2005
SP  - 163
EP  - 177
VL  - 21
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2005__21_2_a2/
LA  - en
ID  - JAC_2005__21_2_a2
ER  - 
%0 Journal Article
%A Bessenrodt, Christine
%A Olsson, Jørn B.
%A Stanley, Richard P.
%T Properties of some character tables related to the symmetric groups
%J Journal of Algebraic Combinatorics
%D 2005
%P 163-177
%V 21
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2005__21_2_a2/
%G en
%F JAC_2005__21_2_a2
Bessenrodt, Christine; Olsson, Jørn B.; Stanley, Richard P. Properties of some character tables related to the symmetric groups. Journal of Algebraic Combinatorics, Tome 21 (2005) no. 2, pp. 163-177. http://geodesic.mathdoc.fr/item/JAC_2005__21_2_a2/