48 citations · 118 across the 17 of their papers we have counts for
17 papers
A tree-free approach to 3D Yang-Mills Langevin dynamic. Analytic estimates and the existence of a model for a regularity structure
Alexey Sevostyanov
Using the multi-index approach to regularity structures due to F. Otto et al., we construct a regularity structure and a model for it associated to the stochastic Langevin equation…
A generalized semi-infinite Hecke equivalence and the local geometric Langlands correspondence
Alexey Sevostyanov
We introduce a class of equivalences, which we call generalized semi-infinite Hecke equivalences, between certain categories of representations of graded associative algebras which…
Towards non-perturbative quantization and the mass gap problem for the Yang-Mills Field
Alexey Sevostyanov
We reduce the problem of quantization of the Yang-Mills field Hamiltonian to a problem for defining a probability measure on an infinite-dimensional space of gauge equivalence clas…
Q-W-algebras, Zhelobenko operators and a proof of De Concini-Kac-Procesi conjecture
Alexey Sevostyanov
This monograph, along with a self-consistent presentation of the theory of q-W-algebras including the construction of algebraic group analogues of Slodowy slices, contains a descri…
Strictly transversal slices to conjugacy classes in algebraic groups
A. Sevostyanov
We show that for every conjugacy class O in a connected semisimple algebraic group G over a field of characteristic good for G one can find a special transversal slice S to the set…
The geometric meaning of Zhelobenko operators
Alexey Sevostyanov
Let g be the complex semisimple Lie algebra associated to a complex semisimple algebraic group G, b a Borel subalgebra of g, h the Cartan sublagebra contained in b and N the unipot…
Conjugacy classes in Weyl groups and q-W algebras
A. Sevostyanov
We define noncommutative deformations of algebras of functions on certain (finite coverings of) transversal slices to the set of conjugacy classes in an algebraic group…
An equivalence of two mass generation mechanisms for gauge fields
A. Sevostyanov
Two mass generation mechanisms for gauge theories are studied. It is proved that in the abelian case the topological mass generation mechanism introduced in hep-th/9301060, hep-th/…
An analogue of the operator curl for nonabelian gauge groups and scattering theory
A. Sevostyanov
We introduce a new perturbation for the operator curl related to connections with nonabelian gauge groups. We also prove that the perturbed operator is unitary equivalent to the op…
Nonlocal lagrangians and mass generation for gauge fields
A. Sevostyanov
In this paper we study the nonabelian, gauge invariant and asymptotically free quantum gauge theory with a mass parameter introduced in hep-th/0605050. We develop the Feynman diagr…
A mass generation mechanism for gauge fields
A. Sevostyanov
We suggest a new mass generation mechanism for gauge fields. The quantum field theory constructed in this paper is nonabelian, gauge invariant and asymptotically free.
The mass gap problem for the Yang-Mills Field
A. Sevostyanov
We consider the reduced Hamiltonian of the Yang-Mills field on equipped with a Lorentzian metric. We show that the secondary quantized principal term of the Ta…
Regular nilpotent elements and quantum groups
A. Sevostyanov
We suggest new realizations of quantum groups corresponding to complex simple Lie algebras, and of affine quantum groups. These new realizations are labeled by Coxeter elements of…
Reduction of quantum systems with arbitrary first class constraints and Hecke algebras
A. Sevostyanov
We propose a method for reduction of quantum systems with arbitrary first class constraints. An appropriate mathematical setting for the problem is homology of associative algebras…
Towards Drinfeld-Sokolov reduction for quantum groups
A. Sevostyanov
In this paper we study the Poisson-Lie version of the Drinfeld-Sokolov reduction defined in q-alg/9704011, q-alg/9702016. Using the bialgebra structure related to the new Drinfeld…
Drinfeld-Sokolov reduction for difference operators and deformations of W-algebras. II. General Semisimple Case
M. A. Semenov-Tian-Shansky, A. V. Sevostyanov
The paper is the sequel to q-alg/9704011. We extend the Drinfeld-Sokolov reduction procedure to q-difference operators associated with arbitrary semisimple Lie algebras. This leads…
The classical r-matrix method for nonlinear sigma-model
Alexey Sevostyanov
The canonical Poisson structure of nonlinear sigma-model is presented as a Lie-Poisson r-matrix bracket on coadjoint orbits. It is shown that the Poisson structure of this model is…