We propose a conjecture relating two different sets of characters for the complex reflection group . From one side, the characters are afforded by Calogero–Moser cells, a conjectural generalisation of Kazhdan–Lusztig cells for a complex reflection group. From the other side, the characters arise from a level irreducible integrable representations of . We prove this conjecture in some cases: in full generality for and for generic parameters for .
Mots clés : Cellular characters, Complex reflection groups
@article{AMBP_2020__27_1_37_0,
author = {Lacabanne, Abel},
title = {On a conjecture about cellular characters for the complex reflection group $G(d,1,n)$},
journal = {Annales math\'ematiques Blaise Pascal},
pages = {37--64},
publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal},
volume = {27},
number = {1},
year = {2020},
doi = {10.5802/ambp.390},
language = {en},
url = {http://www.numdam.org/articles/10.5802/ambp.390/}
}
TY - JOUR AU - Lacabanne, Abel TI - On a conjecture about cellular characters for the complex reflection group $G(d,1,n)$ JO - Annales mathématiques Blaise Pascal PY - 2020 SP - 37 EP - 64 VL - 27 IS - 1 PB - Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal UR - http://www.numdam.org/articles/10.5802/ambp.390/ DO - 10.5802/ambp.390 LA - en ID - AMBP_2020__27_1_37_0 ER -
%0 Journal Article %A Lacabanne, Abel %T On a conjecture about cellular characters for the complex reflection group $G(d,1,n)$ %J Annales mathématiques Blaise Pascal %D 2020 %P 37-64 %V 27 %N 1 %I Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal %U http://www.numdam.org/articles/10.5802/ambp.390/ %R 10.5802/ambp.390 %G en %F AMBP_2020__27_1_37_0
Lacabanne, Abel. On a conjecture about cellular characters for the complex reflection group $G(d,1,n)$. Annales mathématiques Blaise Pascal, Tome 27 (2020) no. 1, pp. 37-64. doi : 10.5802/ambp.390. http://www.numdam.org/articles/10.5802/ambp.390/
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