Related papers: Quaternionic MUBs in H^2 and their reflection symm…

By analogy with the real and complex affine groups, whose unitary irreducible representations are used to define the one and two-dimensional continuous wavelet transforms, we study here the quaternionic affine group and construct its…

Let $K$ be an imaginary quadratic field. Modular forms for GL(2) over $K$ are known as Bianchi modular forms. Standard modularity conjectures assert that every weight 2 rational Bianchi newform has either an associated elliptic curve over…

We determine the maximal hyperbolic reflection groups associated to the quadratic forms $-3x_0^2 + x_1^2 + ... + x_n^2$, $n \ge 2$, and present the Coxeter schemes of their fundamental polyhedra. These groups exist in dimensions up to 13,…

We explore the enumerative problem of finding lines on cubic surfaces defined by symmetric polynomials. We prove that the moduli space of symmetric cubic surfaces is an arithmetic quotient of the complex hyperbolic line, and determine…

Multi-Higgs models equipped with global symmetry groups, either exact or softly broken, offer a rich framework for constructions beyond the Standard Model and lead to remarkable phenomenological consequences. Knowing all the symmetry…

Collection of (equivariant) $\rm{PL}$-mappings admitting a relative abelian, cyclic, quaternionic, bicyclic, and quaternionic-cyclic structures are constructed.

We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schr\"odinger equations admit separation of variables in polar coordinates and are exactly…

In this work we construct an eigencurve for p-adic modular forms attached to an indefinite quaternion algebra over Q. Our theory includes the definition, both as rules on test objects and sections of line bundle, of p-adic modular forms,…

We establish a correspondence between certain Lie superalgebras with 16 fermionic generators, and half-BPS solutions to supergravities with 32 supersymmetries. Three cases are discussed. For Type IIB supergravity, we relate semi-simple Lie…

We present the simplest non-abelian version of Seiberg-Witten theory: Quaternionic monopoles. These monopoles are associated with Spin^h(4)-structures on 4-manifolds and form finite-dimensional moduli spaces. On a Kahler surface the…

In this paper we determine the group of rational automorphisms of binary cubic and quartic forms with integer coefficients and non-zero discriminant in terms of certain quadratic covariants of cubic and quartic forms. This allows one to…

Let $U$ be an algebraic subgroup of the group of $n\times n$ upper-triangular matrices with units on the diagonal over a finite field of large enough characteristic, and $\mathfrak{n}$ be the Lie algebra of $U$. The main tool in…

We classify all complete projective special real manifolds with reducible cubic potential, obtaining four series. For two of the series the manifolds are homogeneous, for the two others the respective automorphism group acts with…

We study the chiral rings in N=2 and N=4 superconformal algebras. The chiral primary states of N=2 superconformal algebras realized over hermitian triple systems are given. Their coset spaces G/H are hermitian symmetric which can be compact…

Spin$^h$ manifolds are the quaternionic analogue to Spin$^c$ manifolds. We compute the spin$^h$ bordism groups at the prime 2 by proving a structure theorem for the cohomology of the spin$^h$ bordism spectrum $\mathrm{MSpin}^h$ as a module…

An important problem in quaternionic hyperbolic geometry is to classify ordered $m$-tuples of pairwise distinct points in the closure of quaternionic hyperbolic n-space, $\overline{{\bf H}_\bh^n}$, up to congruence in the holomorphic…

We give explicit bijective correspondences between three families of objects: certain pairs of quaternions, which we regard as spinors; certain flags in (1+4)-dimensional Minkowski space; and horospheres in 4-dimensional hyperbolic space…

Using the rings of Lipschitz and Hurwitz integers $\mathbb{H}(\mathbb{Z})$ and $\mathbb{H}ur(\mathbb{Z})$ in the quaternion division algebra $\mathbb{H}$, we define several Kleinian discrete subgroups of $PSL(2,\mathbb{H})$

In this note we investigate three new pencils of symmetric surfaces in complex projective three-space. These have degree 6, 8 resp. 12 and are invariant under the action of subgroups of SO(4) containing the Heisenberg group. The pencils of…

There are 13 equivalence classes of 2D second order quantum and classical superintegrable systems with nontrivial potential, each associated with a quadratic algebra of hidden symmetries. We study the finite and infinite irreducible…