Multiplicity one theorems: the Archimedean case
By Binyong Sun. 2009
189 citations recorded by the source corpus.
Let G be one of the classical Lie groups GLn+1(R), GLn+1(C), U(p;q+1), O(p;q+1), On+1(C), SO(p;q+1), SOn+1(C), and let G 0 be respectively the subgroup GLn(R), GLn(C), U(p;q), O(p;q), On(C), SO(p;q), SOn(C), embedded in G in the standard way. We show that every irreducible Casselman-Wallach representation of G 0 occurs with multiplicity at most one in every irreducible Casselman-Wallach representation of G. Similar results are proved for the Jacobi groups GLn(R)nH2n+1(R), GLn(C)n H2n+1(C), U(p;q)nH2p+2q+1(R), Sp2n(R)nH2n+1(R), Sp2n(C)nH2n+1(C), with their respective subgroups GLn(R), GLn(C), U(p;q), Sp2n(R), and Sp2n(C).
View Paper: https://www.semanticscholar.org/paper/ea8679e52edc9d46159587e0653e551078cc8151
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Citations in the corpus
- The orbit method and analysis of automorphic forms (2018, background): “We assume that representations of G have “multiplicity-free restrictions” to H , as happens in the indicated example (see [92] for a precise statement and proof).”
- Fourier transform and the global Gan–Gross–Prasad conjecture for unitary groups (2014, unknown): “By the multiplicity-one result of [3] and [48], we have dim HomHvpπv,Cq ď 1.”
- CLASSIFICATION OF FINITE-MULTIPLICITY SYMMETRIC PAIRS (2013, background): “The implication (iii) ⇒ (ii) was proved in Sun–Zhu [20].”