Related papers: Seidel elements and mirror transformations
The maximal symmetry of a quantum system with Heisenberg commutation relations is given by the projective representations of the automorphism group of the Weyl-Heisenberg algebra. The automorphism group is the central extension of the…
The Goos-H\"anchen (GH) shift and the Imbert-Fedorov (IF) shift are optical phenomena which describe the longitudinal and transverse lateral shifts at the reflection interface, respectively. Here, we report the GH and IF shifts in Weyl…
The fractional Hilbert transforms plays an important role in optics and signal processing. In particular the analytic signal proposed by Gabor has as a key component the Hilbert transform. The higher dimensional Hilbert transform is the…
We study a general phase transition between spinless topological nodal-line semimetal and Weyl semimetal phases. We classify topological nodal lines into two types based on their positions and shapes, and their phase transitions depends on…
In this article we describe the $\tG\times \tG$-equivariant $K$-ring of $X$, where $\tG$ is a {\it factorial} cover of a connected complex reductive algebraic group $G$, and $X$ is a regular compactification of $G$. Furthermore, using the…
We give a brief introduction to Hamiltonian optics and Lie algebraic methods. We use these methods to describe the operators governing light propagation, refraction and reflection in phase space. The method offers a systematic way to find…
We present a formalism that leads very naturally to a hierarchical description of the different contrast structures in images, providing precise definitions of sharp edges and other texture components. Within this formalism, we achieve a…
In this paper we prove a formula relating the equivariant Euler characteristic of $K$-theoretic stable envelopes to an object known as the index vertex for the cotangent bundle of the full flag variety. Our formula demonstrates that the…
We generalized the construction of deformations of affine toric varieties of K. Altmann and our previous construction of deformations of weak Fano toric varieties to the case of arbitrary toric varieties by introducing the notion of…
Friedel's law guarantees an inversion-symmetric diffraction pattern for thin, light materials where a kinematic approximation or a single-scattering model holds. Typically, breaking Friedel symmetry is ascribed to multiple scattering events…
This is a paper in a series systematically to study toroidal vertex algebras. Previously, a theory of toroidal vertex algebras and modules was developed and toroidal vertex algebras were explicitly associated to toroidal Lie algebras. In…
We consider a topological integral transform of Bessel (concentric isospectral sets) type and Fourier (hyperplane isospectral sets) type, using the Euler characteristic as a measure. These transforms convert constructible $\zed$-valued…
This study is motivated by the researches in the field of invariants of geodesic and conformal mappings presented in (T. Y. Thomas, [22]) and (H. Weyl, [25]). The Thomas projective parameter and the Weyl projective tensor are generalized in…
We study the motivic Serre invariant of a smoothly bounded algebraic or rigid variety $X$ over a complete discretely valued field $K$ with perfect residue field $k$. If $K$ has characteristic zero, we extend the definition to arbitrary…
In this paper we consider the so-called crystallographic Radon transform (or crystallographic $X$-ray transform) and totally geodesic Radon transform on the group of rotations SO(3). As we show both of these transforms naturally appear in…
We consider four (real or complex) dimensional hyper-K\"ahler metrics with a conformal symmetry K. The three-dimensional space of orbits of K is shown to have an Einstein-Weyl structure which admits a shear-free geodesics congruence for…
The G\"odel-type metrices are considered as backgrounds of the sigma-models. In the conformal field theory such backgrounds are deformed by the exactly marginal operators. We examinate, how the closed time-like curves (CTC's) transform…
Motivated by Aganagic's equivariant mirror symmetry for certain Coulomb branches of a $3d$ $\mathcal{N}= 4$ gauge quiver theory, we would like to propose a set of ideas towards an extension of Aganagic's proposal to Hitchin systems. At the…
We solved the long-standing problem of describing the cohomology ring of semiample hypersurfaces in complete simplicial toric varieties. Also, the monomial-divisor mirror map is generalized to a map between the whole Picard group and the…
This paper explores homological mirror symmetry for weighted blowups of toric varieties. It will be shown that both the A-model and B-model categories have natural semiorthogonal decompositions. An explicit equivalence of the right…