We derive a formula for the entries in the change-of-basis matrix between Young's seminormal and natural representations of the symmetric group. These entries are determined as sums over weighted paths in the weak Bruhat graph on standard tableaux, and we show that they can be computed recursively as the weighted sum of at most two previously-computed entries in the matrix. We generalize our results to work for affine Hecke algebras, Ariki-Koike algebras, Iwahori-Hecke algebras, and complex reflection groups given by the wreath product of a finite cyclic group with the symmetric group.
@article{10_37236_10081,
author = {Sam Armon and Tom Halverson},
title = {Transition matrices between {Young's} natural and seminormal representations},
journal = {The electronic journal of combinatorics},
year = {2021},
volume = {28},
number = {3},
doi = {10.37236/10081},
zbl = {1470.05168},
url = {http://geodesic.mathdoc.fr/articles/10.37236/10081/}
}
TY - JOUR
AU - Sam Armon
AU - Tom Halverson
TI - Transition matrices between Young's natural and seminormal representations
JO - The electronic journal of combinatorics
PY - 2021
VL - 28
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/10081/
DO - 10.37236/10081
ID - 10_37236_10081
ER -
%0 Journal Article
%A Sam Armon
%A Tom Halverson
%T Transition matrices between Young's natural and seminormal representations
%J The electronic journal of combinatorics
%D 2021
%V 28
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/10081/
%R 10.37236/10081
%F 10_37236_10081
Sam Armon; Tom Halverson. Transition matrices between Young's natural and seminormal representations. The electronic journal of combinatorics, Tome 28 (2021) no. 3. doi: 10.37236/10081
