Related papers: Supersymmetry and algebraic deformations
We extend the deformation theory algorithm of matrix factorizations to systems with more than one D-brane. The obstructions to the deformations are F-term equations which can be integrated to an effective superpotential. We demonstrate the…
We study O'Grady examples of irreducible symplectic varieties: we establish that both of them can be deformed into lagrangian fibrations. We analyse in detail the topology of the six dimensional example: in particular we compute its Euler…
Deforming the algebraic structure of geometric algebra on the phase space with a Moyal product leads naturally to supersymmetric quantum mechanics in the star product formalism.
We extend the construction of 2D superintegrable Hamiltonians with separation of variables in spherical coordinates using combinations of shift, ladder, and supercharge operators to models involving rational extensions of the two-parameter…
The supersymmetrical approach is used to analyse a class of two-dimensional quantum systems with periodic potentials. In particular, the method of SUSY-separation of variables allowed us to find a part of the energy spectra and the…
We define B\"acklund--Darboux transformations in Sato's Grassmannian. They can be regarded as Darboux transformations on maximal algebras of commuting ordinary differential operators. We describe the action of these transformations on…
We consider a one-dimensional Osp($N|2M$) pseudoparticle mechanical model which may be written as a phase space gauge theory. We show how the pseudoparticle model naturally encodes and explains the two-dimensional zero curvature approach to…
Using the notion of a gauge connection on a flat superspace, we construct a general class of noncommutative ($D=2,$ $\mathcal{N}=1$) supertranslation algebras generalizing the ordinary algebra by inclusion of some new bosonic and fermionic…
General Relativity in 4 dimensions can be equivalently described as a dynamical theory of SO(3)-connections rather than metrics. We introduce the notion of asymptotically hyperbolic connections, and work out an analog of the…
We revisit the algebraic description of shape invariance method in one-dimensional quantum mechanics. In this note we focus on four particular examples: the Kepler problem in flat space, the Kepler problem in spherical space, the Kepler…
Using Darboux transformation one can construct infinite family of potentials which lead to the flat spectrum of scalar field fluctuations with arbitrary multiple precision, and, at the same time, with "essentially blue" spectrum of…
We introduce deformations of Kazhdan-Lusztig elements and specialised nonsymmetric Macdonald polynomials, both of which form a distinguished basis of the polynomial representation of a maximal parabolic subalgebra of the Hecke algebra. We…
This thesis is devoted to the study of the deformation and rigidity of infinite dimensional Lie algebras which are not subject to the Hochschild-Serre factorization theorem. In particular, we consider $bms_{3}$, Virasoro-Kac-Moody and…
We introduce the formalism of differential conformal superalgebras, which we show leads to the "correct" automorphism group functor and accompanying descent theory in the conformal setting. As an application, we classify forms of N=2 and…
We study Darboux transformations for the two boson (TB) hierarchy both in the scalar as well as in the matrix descriptions of the linear equation. While Darboux transformations have been extensively studied for integrable models based on…
We study the N=2 four-dimensional superconformal index in various interesting limits, such that only states annihilated by more than one supercharge contribute. Extrapolating from the SU(2) generalized quivers, which have a Lagrangian…
Unfolding singular points in linear differential equations is a classical technique for studying the properties of irregular singularities by relating them to regular singularities. In this paper, we propose a general framework for…
We study Schubert polynomials using geometry of infinite-dimensional flag varieties and degeneracy loci. Applications include Graham-positivity of coefficients appearing in equivariant coproduct formulas and expansions of back-stable and…
In this study, we firstly establish the well-posedness of a degenerate parabolic equation under Dirichlet boundary conditions. Following this, we introduce a shape design problem, which acts as a framework for approximating the degenerate…
By considering $p,q$-deformed and $\mu$-deformed algebras we propose an association of them to form a hybrid deformed algebra. The increased number of available parameters can provide us with a richer tool to investigate new scenarios…