TY - JOUR
T1 - Murnaghan-Kirillov theory for depth-zero supercuspidal representations
T2 - Reduction to Lusztig functions
AU - Debacker, Stephen
AU - Kazhdan, David
PY - 2011/9
Y1 - 2011/9
N2 - The goal of Murnaghan-Kirillov theory is to associate to an irreducible smooth representation of a reductive p-adic group a family of regular semisimple orbital integrals in the Lie algebra with the following property: the character of π is given, on a well determined set, by an explicit combination of the Fourier transforms of these orbital integrals. Subject to certain restrictions, we adapt arguments of Waldspurger to show that, for depth-zero irreducible smooth supercuspidal representations, this problem may be reduced to a similar one for distributions associated to Lusztig functions.
AB - The goal of Murnaghan-Kirillov theory is to associate to an irreducible smooth representation of a reductive p-adic group a family of regular semisimple orbital integrals in the Lie algebra with the following property: the character of π is given, on a well determined set, by an explicit combination of the Fourier transforms of these orbital integrals. Subject to certain restrictions, we adapt arguments of Waldspurger to show that, for depth-zero irreducible smooth supercuspidal representations, this problem may be reduced to a similar one for distributions associated to Lusztig functions.
KW - character
KW - depth-zero
KW - Harmonic analysis
KW - reductive p-adic group
KW - representation
KW - supercuspidal
UR - http://www.scopus.com/inward/record.url?scp=80051903045&partnerID=8YFLogxK
U2 - 10.1007/s00031-011-9155-4
DO - 10.1007/s00031-011-9155-4
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AN - SCOPUS:80051903045
SN - 1083-4362
VL - 16
SP - 737
EP - 766
JO - Transformation Groups
JF - Transformation Groups
IS - 3
ER -