Scalar irreducibility of eigenspaces on the tangent space of a reductive symmetric space
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Scalar irreducibility of eigenspaces on the tangent space of a reductive symmetric space. / Schlichtkrull, Henrik; Stetkær, Henrik.
I: Journal of Functional Analysis, Bind 74, Nr. 2, 10.1987, s. 292-299.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Scalar irreducibility of eigenspaces on the tangent space of a reductive symmetric space
AU - Schlichtkrull, Henrik
AU - Stetkær, Henrik
PY - 1987/10
Y1 - 1987/10
N2 - Let X0 be the tangent space at eH of the reductive symmetric space G H, and let G0 denote the group of affine transformations of X0 generated by the translations and the natural action of H. We show that any joint eigenspace of the G0-invariant differential operators on X0 is scalarly irreducible under the action of G0. This holds in particular for a Riemannian symmetric space of the non-compact type, where G0 is the Cartan motion group.
AB - Let X0 be the tangent space at eH of the reductive symmetric space G H, and let G0 denote the group of affine transformations of X0 generated by the translations and the natural action of H. We show that any joint eigenspace of the G0-invariant differential operators on X0 is scalarly irreducible under the action of G0. This holds in particular for a Riemannian symmetric space of the non-compact type, where G0 is the Cartan motion group.
UR - http://www.scopus.com/inward/record.url?scp=38249035199&partnerID=8YFLogxK
U2 - 10.1016/0022-1236(87)90026-7
DO - 10.1016/0022-1236(87)90026-7
M3 - Journal article
AN - SCOPUS:38249035199
VL - 74
SP - 292
EP - 299
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 2
ER -
ID: 304299028