Related papers: Quantization commutes with reduction in the non-co…
In a joint paper P. Pand\v{z}i\'c and D. Renard proved that holomorphic and antiholomorphic discrete series representations can be constructed via algebraic Dirac induction. The group $SU(2,1)$, except for those two types, also has a third…
I present a method of performing geometric quantization using cohomology groups extended via coefficient groups of different types. This is possible according to the Universal Coefficient Theorem (UTC). I also show that by using this method…
We give density results for automorphic representations of Hilbert modular groups. In particular, we show that there are infinitely many automorphic representations that have a prescribed discrete series factor at some (but not all) real…
For quantum Hamiltonian reductions in arbitrary characteristics, it is known that derived localization holds if and only if the algebra of global sections has finite global dimension. In this paper we provide an alternative characterization…
We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…
We briefly report on our result that, if there exists a realization of a Hopf algebra $H$ in a $H$-module algebra $A$, then their cross-product is equal to the product of $A$ itself with a subalgebra isomorphic to $H$ and commuting with…
We introduce the notion of geometric pseudo-quantisation based on geometric quantisation with a weakened curvature condition. We show how such a structure arises naturally from simple deformations of the symplectic structure and pullbacks…
Pseudo-automorphisms are birational transformations acting as regular automorphisms in codimension 1. We import ideas from geometric group theory to prove that a group of birational transformations that satisfies a fixed point property on…
We prove that rational and 1-rational singularities of complex spaces are stable under taking quotients by holomorphic actions of reductive and compact Lie groups. This extends a result of Boutot to the analytic category and yields a…
In this paper we consider a two component scalar field theory, with noncommutativity in its conjugate momentum space. We quantize such a theory in a compact space with the help of dressing transformations and we reveal a significant effect…
Commutativity gadgets provide a technique for lifting classical reductions between constraint satisfaction problems to quantum-sound reductions between the corresponding nonlocal games. We develop a general framework for commutativity…
We study modules over stacks of deformation quantization algebroids on complex Poisson manifolds. We prove finiteness and duality theorems in the relative case and construct the Hochschild class of coherent modules. We prove that this class…
The complement of a complex hyperplane arrangement is known to be homotopic to a minimal CW complex. There are several approaches to the minimality. In this paper, we restrict our attention to real two dimensional cases, and introduce the…
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…
Free noncommutative fields constitute a natural and interesting example of constrained theories with higher derivatives. The quantization methods involving constraints in the higher derivative formalism can be nicely applied to these…
In this paper we continue the development of Quantum Holonomy Theory, which is a candidate for a fundamental theory, by constructing separable strongly continuous representations of its algebraic foundation, the quantum…
The need for a mathematically rigorous quantization procedure of singular spaces and incomplete motions is pointed out in connection with quantum cosmology. We put our previous suggestion for such a procedure, based on the theory of induced…
The groupoid approach to noncommutative unification of general relativity with quantum mechanics is compared with the canonical gravity quantization. It is shown that by restricting the corresponding noncommutative algebra to its…
The relational version of the modal interpretation offers both a consistent quantum ontology and solution for quantum paradoxes within the framework of nonrelativistic quantum mechanics. In the present paper this approach is generalized for…
We show that for a special class of geometric quantizations with "small" quantum errors, the quantum classical correspondence gives rise to an asymptotic projective representation of the group of Hamiltonian diffeomorphisms. As an…