A CLT Plancherel representations of the infinite-dimensional unitary group

Infinite-dimensional Group Representations

Article Representations of the Infinite Unitary Group from Constrained Quantization

We attempt to reconstruct the irreducible unitary representations of the Banach Lie group U 0 (H) of all unitary operators U on a separable Hilbert space H for which U ? I is compact, originally found by Kirillov and Ol'shanskii, through constrained quantization of its coadjoint orbits. For this purpose the coadjoint orbits are realized as Marsden-Weinstein quotients. The unconstrained system, ...

Representations of the Infinite Unitary Group from Constrained Quantization

We attempt to reconstruct the irreducible unitary representations of the Banach Lie group U0(H) of all unitary operators U on a separable Hilbert space H for which U − I is compact, originally found by Kirillov and Ol’shanskii, through constrained quantization of its coadjoint orbits. For this purpose the coadjoint orbits are realized as Marsden-Weinstein quotients. The unconstrained system, gi...

Disjointness of representations arising in harmonic analysis on the infinite-dimensional unitary group

In the context of the problem of harmonic analysis on the group U(∞) a family of representations Tz,w was constructed and studied in the papers [Olsh2] and [BO]. These representations depend on two complex parameters and provide a natural generalization of the regular representation for the case of “big” group U(∞). The representation Tz,w does not change if z or w is replaced by z or w, respec...

Low - Dimensional Unitary Representations Of

We characterize all simple unitarizable representations of the braid group B 3 on complex vector spaces of dimension d ≤ 5. In particular, we prove that if σ 1 and σ 2 denote the two generating twists of B 3 , then a simple representation ρ : B 3 → GL(V) (for dim V ≤ 5) is unitarizable if and only if the eigenvalues λ 1 , λ 2 ,. .. , λ d of ρ(σ 1) are distinct, satisfy |λ i | = 1 and µ (d) 1i >...