TY - JOUR
T1 - THE ALGEBRA OF CONJUGACY CLASSES OF THE WREATH PRODUCT OF A FINITE GROUP WITH THE SYMMETRIC GROUP
AU - Tout, Omar
N1 - Publisher Copyright:
© Rocky Mountain Mathematics Consortium.
PY - 2023
Y1 - 2023
N2 - Let G be a finite group. In this expository paper, we provide a detailed proof of the polynomiality property of the structure coefficients of the center of the wreath product G o Sn algebra. Our main tool is a universal combinatorial algebra which projects onto the center of the group G o Sn algebra for every n. We show that this universal algebra is isomorphic to the algebra of shifted symmetric functions on jG?j alphabets.
AB - Let G be a finite group. In this expository paper, we provide a detailed proof of the polynomiality property of the structure coefficients of the center of the wreath product G o Sn algebra. Our main tool is a universal combinatorial algebra which projects onto the center of the group G o Sn algebra for every n. We show that this universal algebra is isomorphic to the algebra of shifted symmetric functions on jG?j alphabets.
KW - character theory
KW - partial permutations
KW - shifted symmetric functions
KW - structure coefficients
KW - wreath product
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U2 - 10.1216/rmj.2023.53.561
DO - 10.1216/rmj.2023.53.561
M3 - Article
AN - SCOPUS:85166429332
SN - 0035-7596
VL - 53
SP - 561
EP - 577
JO - Rocky Mountain Journal of Mathematics
JF - Rocky Mountain Journal of Mathematics
IS - 2
ER -