Related papers: $\Uh$ invariant Quantization of Coadjoint Orbits a…

The first obstacle in building a Geometric Quantization theory for nilpotent orbits of a real semisimple Lie group has been the lack of an invariant polarization. In order to generalize the Fock space construction of the quantum mechanical…

In this paper we are mainly concerned with the study of polarizations (in general of higher-order type) on a connected Lie group with a U(1)-principal bundle structure. The representation technique used here is formulated on the basis of a…

We compute the factorisation homology of the four-punctured sphere and punctured torus over the quantum group $\mathcal{U}_q(\mathfrak{sl}_2)$ explicitly as categories of equivariant modules using the framework of `Integrating Quantum…

We study the quantization of spaces whose K-theory in the classical limit is the ring of dual numbers $\mathbb{Z}[t]/(t^2)$. For a compact Hausdorff space we recall necessary and sufficient conditions for this to hold. For a compact quantum…

Generalizing deformation quantizations with separation of variables of a K\"ahler manifold $M$, we adopt Fedosov's gluing argument to construct a category $\mathsf{DQ}$, enriched over sheaves of $\mathbb{C}[[\hbar]]$-modules on $M$, as a…

The purpose of this paper is to propose a sheaf theoretic approach to the theory of quantum principal bundles over non affine bases. We study the quantization of principal bundles G -> G/P, where G is a semisimple group and P a parabolic…

Let $\Uq$ be a quantum group. Regarding a (noncommutative) space with $\Uq$-symmetry as a $\Uq$-module algebra $A$, we may think of equivariant vector bundles on $A$ as projective $A$-modules with compatible $\Uq$-action. We construct an…

We study the virtual Euler characteristics of sheaves over Quot schemes of curves, establishing that these invariants fit into a topological quantum field theory (TQFT) valued in $\mathbb{Z}[[q]]$. We show that the three-pointed genus-zero…

The irreducible unitary representations of the Banach Lie group $U_0(\H)$ (which is the norm-closure of the inductive limit $\cup_k U(k)$) of unitary operators on a separable Hilbert space $\H$, which were found by Kirillov and Ol'shanskii,…

We obtain a family of strict $\hat G$-invariant products on the space of holomorphic functions on a semisimple coadjoint orbit of a complex connected semisimple Lie group $\hat G$. By restriction, we also obtain strict $G$-invariant…

Given a simple Lie algebra $\gggg$, we consider the orbits in $\gggg^*$ which are of R-matrix type, i.e., which possess a Poisson pencil generated by the Kirillov-Kostant-Souriau bracket and the so-called R-matrix bracket. We call an…

On a prequantizable K\"ahler manifold $(M, \omega, L)$, Chan-Leung-Li constructed a genuine (non-asymptotic) action of a subalgebra of the Berezin-Toeplitz star product on $H^0(M, L^{\otimes k})$ for each level $k$ [14]. We extend their…

We quantize homogeneous vector bundles over an even complex sphere $\mathbb{S}^{2n}$ as one-sided projective modules over its quantized coordinate ring. We realize them in two different ways: as locally finite $\mathbb{C}$-homs between…

In our previous paper, we constructed an explicit GL(n)-equivariant quantization of the Kirillov--Kostant-Souriau bracket on a semisimple coadjoint orbit. In the present paper, we realize that quantization as a subalgebra of endomorphisms…

We consider a class of homogeneous manifolds over a simple Lie group which appears in the problem of classification of homogeneous manifolds with reductive subgroups of maximal rank as stabilizer of a point. We prove that any manifold of…

A strong version of the quantization conjecture of Guillemin and Sternberg is proved. For a reductive group action on a smooth, compact, polarized variety (X,L), the cohomologies of L over the GIT quotient X // G equal the invariant part of…

Let $M$ be a smooth algebraic variety of dimension $2(p+q)$ with an algebraic symplectic form and a compatible deformation quantization $\mathcal{O}_h$ of the structure sheaf. Consider a smooth coisotropic subvariety $j: Y \to M$ of…

Let W be a finite Coxeter group in a Euclidean vector space V, and m a W-invariant Z_+-valued function on the set of reflections in W. Chalyh and Veselov introduced in an interesting algebra Q_m, called the algebra of m-quasiinvariants for…

In this paper we consider the problem of deformation quantization of the algebra of polynomial functions on coadjoint orbits of semisimple lie groups. The deformation of an orbit is realized by taking the quotient of the universal…

We consider a smooth Lagrangian subvariety Y in a smooth algebraic variety X with an algebraic symplectic from. For a vector bundle E on Y and a choice Oh of deformation quantization of the structure sheaf of X, we establish when E admits a…