Related papers: Special geometry, cubic polynomials and homogeneou…
We introduce a class of potential submanifolds in pseudo-Euclidean spaces (each N-dimensional potential submanifold is a special flat torsionless submanifold in a 2N-dimensional pseudo-Euclidean space) and prove that each N-dimensional…
We introduce curvature-adapted foliations of complex hyperbolic space and study some of their properties. Generalized pseudo-Einstein hypersurfaces of complex hyperbolic space are classified. Analogous results for curvature-adapted…
In this paper we give a general construction of transcendental lattices for K3 surfaces with real multiplication by arbitrary field up to degree 6 along with formula for their discriminants. We also show that all simple Abelian fourfolds…
A general theory of matrix-spherical functions for dual Hopf algebras and right coideal subalgebras is developed. We establish their existence and define their orthogonality relations. When specialized to Kolb and Letzter's quantum…
We consider the dimensional reduction to D = 3 of four maximal-rank supergravities which preserve minimal supersymmetry in D = 11, 7, 5 and 4. Such "curious" theories were investigated some time ago, and the four-dimensional one corresponds…
The decomposition of the polynomials on the quaternionic unit sphere in $\Hd$ into irreducible modules under the action of the quaternionic unitary (symplectic) group and quaternionic scalar multiplication has been studied by several…
In our joint papers [FL1-FL2] we revive quaternionic analysis and show deep relations between quaternionic analysis, representation theory and four-dimensional physics. As a guiding principle we use representation theory of various real…
The automorphisms of all 4-dimensional, real Lie Algebras are presented in a comprehensive way. Their action on the space of $4\times 4$, real, symmetric and positive definite, matrices, defines equivalence classes which are used for the…
In loop quantum gravity, states of quantum geometry are represented by classes of knotted graphs, equivalent under diffeomorphisms. Thus, it is worthwhile to enumerate and distinguish these classes. This paper looks at the case of 4-regular…
We develop further quaternionic analysis introducing left and right doubly regular functions. We derive Cauchy-Fueter type formulas for these doubly regular functions that can be regarded as another counterpart of Cauchy's integral formula…
This paper is subsequent to [5]. In this paper, we extend the classification of hyperbolic Dehn fillings with sufficiently large coefficients by addressing the remaining case not covered in [5]. Specifically, by considering the case in…
Quantum homogeneous supervector bundles arising from the quantum general linear supergoup are studied. The space of holomorphic sections is promoted to a left exact covariant functor from a category of modules over a quantum parabolic…
We conclude the classification of cohomogeneity one actions on symmetric spaces of rank one by classifying cohomogeneity one actions on quaternionic hyperbolic spaces up to orbit equivalence. As a by-product of our proof, we produce…
We classify, up to isometric congruence, the homogeneous hypersurfaces in the Riemannian symmetric spaces $\mathrm{SL}(3,\mathbb{H})/\mathrm{Sp}(3), \hspace{1pt} \mathrm{SO}(5,\mathbb{C})/\mathrm{SO}(5),$ and…
This article investigates the holonomy groups of K-contact sub-pseudo-Riemannian manifolds. The primary result is a proof that the horizontal holonomy group either coincides with the adapted holonomy group or acts as its normal subgroup of…
In this paper we show that totally geodesic subspaces determine the commensurability class of a standard arithmetic hyperbolic $n$-orbifold, $n\ge 4$. Many of the results are more general and apply to locally symmetric spaces associated to…
The categories of real and of complex Hilbert spaces with bounded linear maps have received purely categorical characterisations by Chris Heunen and Andre Kornell. These characterisations are achieved through Sol\`er's theorem, a result…
We organize the homogeneous special geometries, describing as well the couplings of D=6, 5, 4 and 3 supergravities with 8 supercharges, in a small number of universality classes. This relates manifolds on which similar types of dynamical…
Consider the $3$-dimensional $\mathcal N=4$ supersymmetric gauge theory associated with a compact Lie group $G_c$ and its quaternionic representation $\mathbf M$. Physicists study its Coulomb branch, which is a noncompact hyper-K\"ahler…
In the present discussion, we have studied the Z2-grading of quaternion algebra (H). We have made an attempt to extend the quaternion Lie algebra to the graded Lie algebra by using the matrix representations of quaternion units. The…