Related papers: Connections on Cahen-Wallach spaces

We develop the differential theory of complex spinorial forms associated with irreducible complex spinors across all dimensions and signatures. This framework enables the study of constrained parallelicity conditions for irreducible complex…

We use techniques of Alper-Hall-Rydh to prove a local structure theorem for smooth morphisms between smooth stacks around points with linearly reductive stabilizers. This implies that the good moduli space of a smooth stack over a base has…

We consider an involutive automorphism of the conformal algebra and the resulting symmetric space. We display a new action of the conformal group which gives rise to this space. The space has an intrinsic symplectic structure, a…

We consider Brownian motions and other processes (Ornstein-Uhlenbeck processes, spherical Brownian motions) on various sets of symmetric matrices constructed from algebra structures, and look at their associated spectral measure processes.…

Quaternionic and octonionic realizations of Clifford algebras and spinors are classified and explicitly constructed in terms of recursive formulas. The most general free dynamics in arbitrary signature space-times for both quaternionic and…

Some of the well known Fefferman like constructions of parabolic geometries end up with a new structure on the same manifold. In this paper, we classify all such cases with the help of the classical Onishchik's lists \cite{onish1} and we…

Causal fermion systems and Riemannian fermion systems are proposed as a framework for describing non-smooth geometries. In particular, this framework provides a setting for spinors on singular spaces. The underlying topological structures…

We study the connected components of the space of higher spin bundles on hyperbolic Klein surfaces. A Klein surface is a generalisation of a Riemann surface to the case of non-orientable surfaces or surfaces with boundary. The category of…

The theory of spinors is developed for locally anisotropic (la) spaces, in brief la-spaces, which in general are modeled as vector bundles provided with nonlinear and distinguished connections and metric structures (such la-spaces contain…

We address the construction of smooth bundles of fermionic Fock spaces, a problem that appears frequently in fermionic gauge theories. Our main motivation is the spinor bundle on the free loop space of a string manifold, a structure…

We obtain two partial answers to the 3-space problem for isomorphic polyhedrality: (1) every twisted sum of $C(\alpha)$, $\alpha<\omega_1$, with a separable isomorphically polyhedral space with the BAP, is isomorphically polyhedral. (2)…

This article surveys the use of configuration space integrals in the study of the topology of knot and link spaces. The main focus is the exposition of how these integrals produce finite type invariants of classical knots and links. More…

One particular approach to quantum groups (matrix pseudo groups) provides the Manin quantum plane. Assuming an appropriate set of non-commuting variables spanning linearly a representation space one is able to show that the endomorphisms on…

Exterior differential forms with values in the (Kostant's) symplectic spinor bundle on a manifold with a given metaplectic structure are decomposed into invariant subspaces. Projections to these invariant subspaces of a covariant derivative…

We study the holomorphic symplectic geometry of (the smooth locus of) the space of holomorphic sections of a twistor space with rotating circle action. The twistor space carries a line bundle with meromorphic connection constructed by…

We describe spinors in Minkowskian spaces with arbitrary signature and their role in the classification of space-time superalgebras and their R-symmetries in any dimension.

The Seiberg-Witten equations that have recently found important applications for four-dimensional geometry are the Euler-Lagrange equations for a functional involving a connection $A$ on a line bundle $L$ and a section $\phi$ of another…

We establish a Bruhat decomposition indexed by the wreath product $\Sigma_m\wr \Sigma_d$ between two symmetric groups -- note that $\Sigma_m\wr \Sigma_d$ is not a Coxeter group in general. We show that such a decomposition affords a…

We define Boolean algebras in the linear context and study its symmetric powers. We give explicit formulae for products in symmetric Boolean algebras of various dimensions. We formulate symmetric forms of the inclusion-exclusion principle.

Based on \cite{DH94}, we introduce a bijective correspondence between first order differential calculi and the graph structure of the symmetric lattice that allows one to encode completely the interconnection structure of the graph in the…