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It is known that all the vector bundles of the title can be obtained by holomorphic induction from representations of a certain parabolic Lie algebra on finite dimensional inner product spaces. The representations, and the induced bundles,…
We study the set of homomorphisms from a fixed finitely generated group into a family of groups which are `uniformly acylindrically hyperbolic'. Our main results reduce this study to sets of homomorphisms which do not diverge in an…
It is shown how to construct *-homomorphic quantum stochastic Feller cocycles for certain unbounded generators, and so obtain dilations of strongly continuous quantum dynamical semigroups on C* algebras; this generalises the construction of…
For manifolds with geodesic flow that is ergodic on the unit tangent bundle, the quantum ergodicity theorem implies that almost all Laplacian eigenfunctions become equidistributed as the eigenvalue goes to infinity. For a locally symmetric…
A simple exactly solvable kinetic model for the non-linear inelastic hard sphere Boltzmann equation is used to explore the relevance of hydrodynamics for a granular gas. The equation predicts a non-trivial homogeneous cooling state (HCS),…
We extend both the Hawking-Penrose Theorem and its generalisation due to Galloway and Senovilla to Lorentzian metrics of regularity $C^1$. For metrics of such low regularity, two main obstacles have to be addressed. On the one hand, the…
A finite group $G$ is called $C$-quasirandom (by Gowers) if all non-trivial irreducible complex representations of $G$ have dimension at least $C$. For any unit $\ell^{2}$ function on a finite group we associate the quantum probability…
The following properties are preserved under elementary equivalence, among finitely generated groups: being hyperbolic (possibly with torsion), being hyperbolic and cubulable, and being a subgroup of a hyperbolic group. In other words, if a…
For an ergodic probability-measure-preserving action $G \curvearrowright (X, \mu)$ of a countable group $G$, we define the Rokhlin entropy $h_G^{\mathrm{Rok}}(X, \mu)$ to be the infimum of the Shannon entropies of countable generating…
For every group $G$, we introduce the set of hyperbolic structures on $G$, denoted $\mathcal{H}(G)$, which consists of equivalence classes of (possibly infinite) generating sets of $G$ such that the corresponding Cayley graph is hyperbolic;…
The classical radial part formula for the invariant differential operators and the K-invariant functions on a Riemannian symmetric space G/K is generalized to some non-invariant cases by use of Cherednik operators and a graded Hecke algebra…
Small perturbations of the homogeneous cooling state (HCS) for a low density granular gas are described by means of the linearized Boltzmann equation. The spectrum of the generator for this dynamics is shown to contain points corresponding…
Let $G$ denote an infinite-dimensional Heisenberg-like group, which is a class of infinite-dimensional step 2 stratified Lie groups. We consider holomorphic functions on $G$ that are square integrable with respect to a heat kernel measure…
Let D be a simply laced Dynkin diagram of rank r whose affinization has the shape of a star (i.e., D4,E6,E7,E8). To such a diagram one can attach a group G whose generators correspond to the legs of the affinization, have orders equal to…
Starting from generic bilinear Hamiltonians, constructed by covariant vector, bivector or tensor fields, it is possible to derive a general symplectic structure which leads to holonomic and anholonomic formulations of Hamilton equations of…
Given an $\infty$-category $\mathcal{C}$ with pullbacks, its $(\infty,2)$-category $\mathbf{Span}(\mathcal{C})$ of spans has the universal property of freely adding right adjoints to morphisms in $\mathcal{C}$ satisfying a Beck--Chevalley…
Given any group $G$, the multiple holomorph $\mathrm{NHol}(G)$ is the normalizer of the holomorph $\mathrm{Hol}(G) = \rho(G)\rtimes \mathrm{Aut}(G)$ in the group of all permutations of $G$, where $\rho$ denotes the right regular…
A new class of analytic, exact, rotating, self-similar and surprisingly simple solutions of non-relativistic hydrodynamics are presented for a three-dimensionally expanding, spheroidally symmetric fireball. These results generalize earlier,…
Based on the generalized kinetic equation for the one-particle distribution function with a small source, the transition from the kinetic to the hydrodynamic description of many-particle systems is performed. The basic feature of this new…
Let $H$ be a Krull monoid with finite class group $G$ and suppose that every class contains a prime divisor. If an element $a \in H$ has a factorization $a=u_1 \cdot \ldots \cdot u_k$ into irreducible elements $u_1, \ldots, u_k \in H$, then…