# SINGULAR CONFORMALLY INVARIANT TRILINEAR FORMS, II THE HIGHER MULTIPLICITY CASE

SINGULAR CONFORMALLY INVARIANT TRILINEAR FORMS, II THE HIGHER MULTIPLICITY CASE Let S be the sphere of dimension n − 1, n ≥ 4. Let π λ λ ∈ ℂ $${\left({\uppi}_{\uplambda}\right)}_{{{}_{\uplambda}}_{\in \mathbb{C}}}$$ be the scalar principal series of representations of the conformal group SO0(1; n), realized on C ∞(S). For λ = (λ1, λ2, λ3,) ∈ ℂ3, let Tri(λ) be the space of continuous trilinear forms on C ∞(S) × C ∞(S) × C ∞(S) which are invariant under πλ1 ⊗ πλ2 ⊗ π λ3. For each value of λ, the dimension of Tri(λ) is computed and a basis of Tri(λ) is described. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Transformation Groups Springer Journals

# SINGULAR CONFORMALLY INVARIANT TRILINEAR FORMS, II THE HIGHER MULTIPLICITY CASE

, Volume 22 (3) – Jul 21, 2016
56 pages

/lp/springer_journal/singular-conformally-invariant-trilinear-forms-ii-the-higher-TJ0ZCxGWZJ
Publisher
Springer US
Subject
Mathematics; Topological Groups, Lie Groups; Algebra
ISSN
1083-4362
eISSN
1531-586X
D.O.I.
10.1007/s00031-016-9404-7
Publisher site
See Article on Publisher Site

### Abstract

Let S be the sphere of dimension n − 1, n ≥ 4. Let π λ λ ∈ ℂ $${\left({\uppi}_{\uplambda}\right)}_{{{}_{\uplambda}}_{\in \mathbb{C}}}$$ be the scalar principal series of representations of the conformal group SO0(1; n), realized on C ∞(S). For λ = (λ1, λ2, λ3,) ∈ ℂ3, let Tri(λ) be the space of continuous trilinear forms on C ∞(S) × C ∞(S) × C ∞(S) which are invariant under πλ1 ⊗ πλ2 ⊗ π λ3. For each value of λ, the dimension of Tri(λ) is computed and a basis of Tri(λ) is described.

### Journal

Transformation GroupsSpringer Journals

Published: Jul 21, 2016

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