Affiliation:
1. Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima Hiroshima, 739-8526, Japan
Abstract
Kazhdan, Kostant, Binegar–Zierau and Kobayashi–Ørsted constructed a distinguished infinite-dimensional irreducible unitary representation π of the indefinite orthogonal group G = O(2p, 2q) for p, q ≥ 1 with p + q > 2, which has the smallest Gelfand–Kirillov dimension 2p + 2q - 3 among all infinite-dimensional irreducible unitary representations of G and hence is called the minimal representation. We consider, for which subgroup G′ of G, the restriction π|G′ is multiplicity-free. We prove that the restriction of π to any subgroup containing the direct product group U(p1) × U(p2) × U(q) for p1, p2 ≥ 1 with p1 + p2 = p is multiplicity-free, whereas the restriction to U(p1) × U(p2) × U(q1) × U(q2) for q1, q2 ≥ 1 with q1 + q2 = q has infinite multiplicities.
Publisher
World Scientific Pub Co Pte Lt
Reference16 articles.
1. Unitarization of a singular representation ofSO(p, q)
2. Tensor Square of the Minimal Representation of O(p, q)
3. Transcending classical invariant theory
4. Homogeneous functions on light cones: the infinitesimal structure of some degenerate principal series representations
5. D. Kazhdan, Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory, Progress in Mathematics 92, eds. Connes (Birkhäuser, Boston, 1990) pp. 125–158.
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Branching laws for small unitary representations of GL(n, ℂ);International Journal of Mathematics;2014-06
2. Varna Lecture on L 2-Analysis of Minimal Representations;Lie Theory and Its Applications in Physics;2013
3. Algebraic Analysis of Minimal Representations;Publications of the Research Institute for Mathematical Sciences;2011