Let $G$ be a finite group acting on the finite set $X$ such that the corresponding (complex) permutation representation is multiplicity free. There is a natural rank and order preserving action of the wreath product $G\sim S_n$ on the generalized Boolean algebra $B_X(n)$. We explicitly block diagonalize the commutant of this action.
@article{10_37236_4831,
author = {Ashish Mishra and Murali K. Srinivasan},
title = {Wreath product action on generalized {Boolean} algebras},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {2},
doi = {10.37236/4831},
zbl = {1327.05339},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4831/}
}
TY - JOUR
AU - Ashish Mishra
AU - Murali K. Srinivasan
TI - Wreath product action on generalized Boolean algebras
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/4831/
DO - 10.37236/4831
ID - 10_37236_4831
ER -
%0 Journal Article
%A Ashish Mishra
%A Murali K. Srinivasan
%T Wreath product action on generalized Boolean algebras
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/4831/
%R 10.37236/4831
%F 10_37236_4831
Ashish Mishra; Murali K. Srinivasan. Wreath product action on generalized Boolean algebras. The electronic journal of combinatorics, Tome 22 (2015) no. 2. doi: 10.37236/4831
