Related papers: The $\mathrm{GL}_4$ Rapoport-Zink Space

For an odd prime $p$, we realize the trivial representation of $\mathrm{GL}_2(\mathbb{Z}/p^n\mathbb{Z})$ on the free $\mathbb{Z}/p^n \mathbb{Z}$-module of rank one as a subquotient of a direct sum of symmetric power representations (twisted…

We study the global structure of moduli spaces of quasi-isogenies of polarized p-divisible groups introduced by Rapoport and Zink. Using the corresponding results for non-polarized p-divisible groups from a previous paper, we determine…

Bound and scattering state Schr\"odinger functions of nonrelativistic quantum mechanics as representation matrix elements of space and time are embedded into residual representations of spacetime as generalizations of Feynman propagators.…

In this note, we study Shimura varieties for the groups $\mathrm{GU}(V)$, where $V$ is a Hermitian space relative to a CM extension $E/E^+$. We give a description of the supersingular locus of the fiber at a prime $\nu$ over $p$ of such a…

Let $\mathfrak{g}$ be a complex semisimple Lie algebra, $G$ a simply connected and connected Lie group with Lie algebra $\mathfrak{g}$ and $V$ a finite dimensional representation. We prove that the zero locus of quadrics containing $G.y$ is…

Let $\F$ be a non-Archimedean locally compact field, $q$ be the cardinality of its residue field, and $\R$ be an algebraically closed field of characteristic $\ell$ not dividing $q$.We classify all irredu\-cible smooth $\R$-representations…

Let O be a complete discrete valuation domain with finite residue field. In this paper we describe the irreducible representations of the groups Aut(M) for any finite O-module M of rank two. The main emphasis is on the interaction between…

A new approach towards the composite structure of quarks and leptons in the context of the higher dimensional unified theories is proposed. Owing to the certain strong dynamics, much like an ordinary QCD, every possible vectorlike…

Let $p$ be a prime number, $K$ a finite extension of $\mathbb{Q}_p$ and $n$ an integer $\geq 2$. We completely and explicitly describe the global sections $\Omega^\bullet$ of the de Rham complex of the Drinfeld space over $K$ in dimension…

We study a Shimura variety attached to a unitary similitude group of a skew-Hermitian form over a totally indefinite quaternion algebra over a totally real number field. We give a necessary and sufficient condition for the existence of…

In "Curves on Heisenberg invariant quartic surfaces in projective 3-space", Eklund showed that a general $(\mathbb{Z}/2\mathbb{Z})^{4}$-invariant quartic K3 surface contains at least $320$ conics. In this paper we analyse the field of…

The existence of a topological double-covering for the $GL(n,R)$ and diffeomorphism groups is reviewed. These groups do not have finite-dimensional faithful representations. An explicit construction and the classification of all…

Among all plastic deformations of the gravitational Lorentz vacuum \cite{wr1} a particular role is being played by conformal deformations. These are conveniently described by using the homogeneous space for the conformal group…

We study the supersingular locus of the Siegel modular variety of genus 3 or 4. More concretely, we decompose the supersingular locus into a disjoint union of the product of a Deligne-Lusztig variety of Coxeter type and a finite-dimensional…

Let $p$ be a prime number and $K$ a finite extension of $\mathbb{Q}_p$. We state conjectures on the smooth representations of $\mathrm{GL}_n(K)$ that occur in spaces of mod $p$ automorphic forms (for compact unitary groups). In particular,…

This paper concerns the characteristic-$p$ fibers of $\mathsf{GU}(3,2)$ Shimura varieties. Such Shimura varieties parametrize abelian varieties in characteristic $p$ of dimension $5$ with an action of signature $(3,2)$ by an order in an…

In this article, we prove a Kudla-Rapoport conjecture for $\mathcal{Y}$-cycles on exotic smooth unitary Rapoport-Zink spaces of odd arithmetic dimension, i.e. the arithmetic intersection numbers for $\mathcal{Y}$-cycles equals the…

We examine the recently found point of intersection between the Z_2 and Z_4 orbifold subvarieties in the K3 moduli space more closely. First we give an explicit identification of the coordinates of the respective Z_2 and Z_4 orbifold…

For an abelian type Shimura variety and an odd prime $p$ of good reduction, we characterize the regularity in codimension one of Zariski closures of Ekedahl--Oort strata in terms of the Frobenius action on the root datum. We give an…

We introduce and study a semigroup structure on the set of irreducible components of the Hurwitz space of marked coverings of a complex projective curve with given Galois group of the coverings and fixed ramification type. As application,…