相关论文: Quantization of geometry associated to the quantiz…
The quantized Knizhnik-Zamolodchikov equation is a difference equation defined in terms of rational $R$ matrices. We describe all singularities of hypergeometric solutions to the qKZ equations.
Correlation functions of gauged WZNW models are shown to satisfy a differential equation, which is a gauge generalization of the Knizhnik-Zamolodchikov equation.
The quantized Knizhnik-Zamolodchikov equations associated with the trigonometric R-matrix or the rational R-matrix of the A-type are considered. Jackson integral representations for solutions of these equations are described. Asymptotic…
We explicitly write dowm integral formulas for solutions to Knizhnik-Zamolodchikov equations with coefficients in non-bounded -- neither highest nor lowest weight -- $\gtsl_{n+1}$-modules. The formulas are closely related to WZNW model at a…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
The basic elements of the geometric approach to a consistent quantization formalism are summarized, with reference to the methods of the old quantum mechanics and the induced representations theory of Lie groups. A possible relationship…
We review results on the Knizhnik-Zamolodchikov (KZ) and dynamical equations, both differential and difference, in the context of the $(gl_k,gl_n)$ duality, and their implications for hypergeometric integrals. The KZ and dynamical equations…
An integral formula for the solutions of Knizhnik-Zamolodchikov (KZ) equation with values in an arbitrary irreducible representation of the symmetric group S_N is presented for integer values of the parameter. The corresponding integrals…
We discuss relations between different formulae for solutions of the Knizhnik-Zamolodchikov differential and the quantum Knizhnik-Zamolodchikov difference equations at level 0 and associated with rational solutions of the Yang-Baxter…
We construct integral representations of solutions to the boundary quantum Knizhnik-Zamolodchikov equations. These are difference equations taking values in tensor products of Verma modules of quantum affine $\mathfrak{sl}_2$, with the…
These notes give an introduction to the quantization procedure called geometric quantization. It gives a definition of the mathematical background for its understanding and introductions to classical and quantum mechanics, to differentiable…
We construct special solutions of the quantum Knizhnik-Zamolodchikov equation on the tensor product of the vector representation of the quantum algebra of type A_{N-1}. They are constructed from non-symmetric Macdonald polynomials through…
We consider the Knizhnik-Zamolodchikov (KZ) and dynamical equations, both differential and difference, in the context of the (gl_k,gl_n) duality. We show that the KZ and dynamical equations naturally exchange under the duality.
We construct an integral representation of solutions of the Knizhnik-Zamolodchikov-Bernard equations, using the Wakimoto modules.
The paper presents shortly the geometric approach to the problem of a general quantization formalism, both physically meaningful and mathematically consistent.
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
We consider the $sl(2)$ quantized Knizhnik-Zamolodchikov equation (qKZ), defined in terms of rational R-matrices. The properties of the equation change when the step of the equation takes a resonance value. In this case the discrete…
Knizhnik-Zamolodchikov-Bernard equations for twisted conformal blocks on compact Riemann surfaces with marked points are written explicitly in a general projective structure in terms of correlation functions in the theory of twisted b-c…
We consider the quantized Knizhnik-Zamolodchikov difference equation (qKZ) with values in a tensor product of irreducible sl(2) modules, the equation defined in terms of rational R-matrices. We solve the equation in terms of…
In this review the foundations of Geometric Quantization are explained and discussed. In particular, we want to clarify the mathematical aspects related to the geometrical structures involved in this theory: complex line bundles, hermitian…