Related papers: Geometric quantization and the generalized Segal-B…

Let $M$ be a compact K\"ahler manifold equipped with a pre-quantum line bundle $L$. In [9], using $T$-symmetry, we constructed a polarization $\mathcal{P}_{\mathrm{mix}}$ on $M$, which generalizes real polarizations on toric manifolds. In…

We analyse the `quantization commutes with reduction' problem (first studied in physics by Dirac, and known in the mathematical literature also as the Guillemin-Sternberg Conjecture) for the conjugate action of a compact connected Lie group…

In this paper, we describe holomorphic quantizations of the cotangent bundle of a symmetric space of compact type $T^*(U/K)\cong U_\mathbb{C}/K_\mathbb{C}$, along Mabuchi rays of $U$-invariant K\"ahler structures. At infinite geodesic time,…

In this note we investigate the image of Sobolev spaces of fractional order on a compact Lie group $ K $ under the Segal-Bargmann transform. We show that the image can be characterised in terms of certain weighted Bergman spaces of…

Let G/K be a Riemannian symmetric space of the complex type, meaning that G is complex semisimple and K is a compact real form. Now let {\Gamma} be a discrete subgroup of G that acts freely and cocompactly on G/K. We consider the…

In this paper we use techniques of geometric quantization to give a geometric interpretation of the Peter--Weyl theorem. We present a novel approach to half-form corrected geometric quantization in a specific type of non-K\"ahler…

We develop a new approach to geometric quantization using the theory of convergence of metric measure spaces. Given a family of K\"ahler polarizations converging to a non-singular real polarization on a prequantized symplectic manifold, we…

A natural one-parameter family of K\"ahler quantizations of the cotangent bundle $T^*K$ of a compact Lie group $K$, taking into account the half-form correction, was studied in \cite{FMMN}. In the present paper, it is shown that the…

We consider the generalized Segal-Bargmann transform C_t for a compact group K, introduced in B. C. Hall, J. Funct. Anal. 122 (1994), 103-151. Let K_C denote the complexification of K. We give a necessary-and-sufficient pointwise growth…

For a symplectic toric manifold we consider half-form quantization in mixed polarizations $\mathcal{P}_\infty$, associated to the action of a subtorus $T^p\subset T^n$. The real directions in these polarizations are generated by components…

In this paper, we study the analytic continuation to complex time of the Hamiltonian flow of certain $G\times T$-invariant functions on the cotangent bundle of a compact connected Lie group $G$ with maximal torus $T$. Namely, we will take…

Let $K$ be a simply connected compact Lie group and $T^{\ast}(K)$ its cotangent bundle. We consider the problem of "quantization commutes with reduction" for the adjoint action of $K$ on $T^{\ast}(K).$ We quantize both $T^{\ast}(K)$ and the…

One introduces the notion of C*-algebra with polarization which could be considered as the quantum Kahler structure. The connection of these algebras with Kostant-Souriou geometric quantization is shown. The theory of polarized C*-algebra…

We introduce a new form of the Segal--Bargmann transform for a Lie group $K$ of compact type. We show that the heat kernel $(\rho_{t}(x))_{t>0,x\in K}$ has a space-time analytic continuation to a holomorphic function \[…

The phase space of a compact, irreducible, simply connected, Riemannian symmetric space admits a natural family of K\"ahler polarizations parametrized by the upper half plane $S$. Using this family, geometric quantization, including the…

It is shown that the heat operator in the Hall coherent state transform for a compact Lie group $K$ is related with a Hermitian connection associated to a natural one-parameter family of complex structures on $T^*K$. The unitary parallel…

In this paper, we begin a quantization program for nilpotent orbits of a real semisimple Lie group. These orbits and their covers generalize the symplectic vector space. A complex structure polarizing the orbit and invariant under a maximal…

In this paper, we study quantization on a compact integral symplectic manifold $X$ with transversal real polarizations. In the case of complex polarizations, namely $X$ is K\"ahler equipped with transversal complex polarizations $T^{1, 0}X,…

Quantization identifies the cotangent bundle of projective space with the (non-Hermitian) rank-$1$ projections of a Hilbert space. We use this identification to study the natural geometric structures of these cotangent bundles and those of…

The bundle map $T^*\hspace{-2pt}\operatorname{U}(n)\longrightarrow\operatorname{U}(n)$ provides a real polarization of the cotangent bundle $T^*\hspace{-2pt}\operatorname{U}(n)$, and yields the geometric quantization…