Geodesic
On the decomposition map for symmetric groups.
Journal of Algebraic Combinatorics, Tome 28 (2008) no. 1, pp. 219-229.

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

Summary: Let $R ^{ d }$ be the $\Bbb $Z-module generated by the irreducible characters of the symmetric group $S _{ d}$ mathcalS_d . We determine bases for the kernel of the decomposition map. It is known that $R ^{ d } \otimes _{\Bbb Z} F$ is isomorphic to the radical quotient of the Solomon descent algebra when $F$ is a field of characteristic zero. We show that when $F$ has prime characteristic and $I _{ br } ^{ d }$ is the kernel of the decomposition map for prime $p$ then $R ^{ d }/ I _{ br } ^{ d } \otimes _{\Bbb Z} F$ is isomorphic to the radical quotient of the $p$-modular Solomon descent algebra.
Classification : 20C20, 20C30, 05E99, 16S99
Keywords: keywords representations of symmetric groups, decomposition map, characters: Brauer characters, symmetric functions, Solomon descent algebra 
@article{JAC_2008__28_1_a1,
     author = {Erdmann, Karin},
     title = {On the decomposition map for symmetric groups.},
     journal = {Journal of Algebraic Combinatorics},
     pages = {219--229},
     publisher = {mathdoc},
     volume = {28},
     number = {1},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2008__28_1_a1/}
}
TY  - JOUR
AU  - Erdmann, Karin
TI  - On the decomposition map for symmetric groups.
JO  - Journal of Algebraic Combinatorics
PY  - 2008
SP  - 219
EP  - 229
VL  - 28
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2008__28_1_a1/
LA  - en
ID  - JAC_2008__28_1_a1
ER  - 
%0 Journal Article
%A Erdmann, Karin
%T On the decomposition map for symmetric groups.
%J Journal of Algebraic Combinatorics
%D 2008
%P 219-229
%V 28
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2008__28_1_a1/
%G en
%F JAC_2008__28_1_a1
Erdmann, Karin. On the decomposition map for symmetric groups.. Journal of Algebraic Combinatorics, Tome 28 (2008) no. 1, pp. 219-229. http://geodesic.mathdoc.fr/item/JAC_2008__28_1_a1/