Central sidonicity for compact Lie groups

Random unitaries, amenable linear groups and Jordan's theorem

“…Giulini and Travaglini [18] improving results due to Price and Rider proved that for any compact connected semisimple Lie group G there are no infinite local Λ p sets for p > 1. Related results appear in [26,34,35,13,20]. Cartwright and McMullen [8] characterized the compact connected groups that admit an infinite local Sidon set, and proved that they contain an infinite Sidon set.…”

Central Interpolation Sets for Compact Groups and Hypergroups

“…Also, if we assume that the degrees of the representations are bounded by 2 N , then the cardinality of {i : σ j • π i = 1} is at most N for each j. These facts, combined with the combinatorial argument described in detail in the proof of Theorem 2.7 of [12], show that {σ j } must contain an infinite subset of either of the following forms:…”

I0 SETS FOR COMPACT, CONNECTED GROUPS: INTERPOLATION WITH MEASURES THAT ARE NONNEGATIVE OR OF SMALL SUPPORT

“…Therefore, we may assume that, for each i, {σ | G i : σ ∈ E} has at most one element. A combinatorial argument shows that such a set contains an infinite subset of the form {χ ⊗ σ i } i where the representations {σ i } are mutually orthogonal and orthogonal to χ (see [6,Theorem 2.7] or [7,Lemma 4.5] for a proof). By Corollary 4.2 {χ ⊗ σ i } i is an infinite set which is cofinitely FZ I 0 (U ) for all open U .…”