The phrase "a unitary representation of" is correct and usable in written English.
It is typically used in mathematical or theoretical contexts, particularly in discussions about group theory and quantum mechanics.
Example: "In the study of symmetries, we often explore a unitary representation of a group acting on a Hilbert space."
Alternatives: "a single representation of" or "a unified representation of".
Let π be a unitary representation of a Lie group G.
Let λ be a finite-dimensional representation of a connected nilpotent group G and U be a unitary representation of G.
In the general case, we characterize Borel sets Ω having this spectral property in terms of a unitary representation of (R,+) acting by local translations.
A unitary representation of the group cannot be determined, since the measure μ is not quasi-invariant with respect to the action of the group G. Consequently, operators of a representation of the Lie algebra and its universal enveloping algebra (in particular, a Laplace operator) are not defined.
We construct, given a Riemannian flag on a smooth manifold X and a compact semi-simple Lie group G, a unitary representation of order 1 of the G-valued gauge group, i.e., of the group of G-valued, compactly supported, smooth mappings on X.
We have the mapping (sigma Grightarrowmathcal{U}(L^{2}(R^{d}))), where (mathcal{U}(L^{2}(R^{d}))) denotes the group of unitary operators on (L^{2}(R^{d})), and it is a unitary representation of the shearlet group.
In representation theory, the Peter Weyl theorem guarantees that any unitary representation of a compact group on a Hilbert space splits as the direct sum of finite-dimensional representations.
But examples of the type (C^*_rho (G)) of algebras generated by a unitary representation (rho ) of G are also interesting.
For a triple (G,τ,S), where G is a Lie group, τ an involutive automorphism of G and S a subsemigroup invariant under the involution s↦s♯="τ(s)−1, a unitary representation π of G on (E,E+,θ) is called reflection positive if θπ(g)θ="π(τ(g)) and π(S E+⊆E+.
This induces a unitary representation D T of the cyclic group Z L which maps the k th power of the generator g ∈ Z L of degree L to D T ( g k ) = U T k.
We show that in the presence of suitable commutator estimates, a projective unitary representation of the Lie algebra of a connected and simply connected Lie group G exponentiates to G. Our proof does not assume G to be finite-dimensional or of Banach Lie type and therefore encompasses the diffeomorphism groups of compact manifolds.
