In this paper, we introduce a study of prolongations of homogeneous vector bundles. We give an alternative approach for the prolongation. For a given homogeneous vector bundle E, we obtain a new homogeneous vector bundle. The homogeneous structure and its corresponding representation are derived. The prolongation of in…
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,657 papers · 148 categories
Trend · papers per month
48 results for “representation homogeneity”
New domains of discontinuity found for Anosov representations.
problem Understanding Anosov representations acting on homogeneous spaces.
method Constructing open domains of discontinuity for Anosov representations acting on specific homogeneous spaces.
result Describes the largest possible open domains of discontinuity for Zariski dense Anosov representations.
Flat semigroups can represent normal weighted homogeneous surface singularities.
problem Representability of flat semigroups in normal weighted homogeneous surface singularities.
method Study of numerical semigroups associated with surface singularities and prove representability conditions.
result A numerical semigroup is representable if and only if it can be written as a quotient of a flat semigroup.
The main result of this paper is the classification of the real irreducible representations of compact Lie groups with vanishing homogeneity rank.
Study equigeodesics on compact homogeneous spaces using Lie algebra properties.
problem Identifying equigeodesic vectors on compact homogeneous spaces.
method Formula for equigeodesic vectors based on isotropy representation and Lie algebra structure.
result Identification of equigeodesic vectors solely through Lie algebra properties.
The 2-parameter family of certain homogeneous Lorentzian 3-manifolds which includes Minkowski 3-space and anti-de Sitter 3-space is considered. Each homogeneous Lorentzian 3-manifold in the 2-parameter family has a solvable Lie group structure with left invariant metric. A generalized integral representation formula wh…
The 2-parameter family of certain homogeneous Lorentzian 3-manifolds which includes Minkowski 3-space, de Sitter 3-space, and Minkowski motion group is considered. Each homogeneous Lorentzian 3-manifold in the 2-parameter family has a solvable Lie group structure with left invariant metric. A generalized integral repre…
The paper constructs CR manifolds with arbitrary Levi nondegeneracy.
problem Creating CR manifolds with specific Levi nondegeneracy properties.
method Using algebras from representations, studying iterated Levi forms, and local model equations.
result Explicit construction and analysis of homogeneous CR manifolds with arbitrary Levi nondegeneracy.
Study Kähler-Ricci flow on rational homogeneous varieties using algebraic geometry and representation theory.
problem Analyzing the Kähler-Ricci flow on rational homogeneous varieties.
method Combining projective algebraic geometry and representation theory of semisimple Lie groups and Lie algebras.
result Explicit description and computation of solutions and geometric quantities along the flow.
The paper explores how AI trading agents' similar information representation can cause financial market instability.
problem Systemic instability in AI-dominated financial markets due to similar information representation.
method Structural multi-agent market model with two-layer decision architecture for AI agents.
result Representation homogeneity can lead to systemic instability in financial markets.
Study invariant spin^r structures on homogeneous spaces.
problem Classify invariant spin^r structures on homogeneous spaces.
method Introduce and study -invariance of spin^r structures on homogeneous spaces.
result Classification of invariant spin^r structures in terms of isotropy representation.
Into this note we collect topics related to homogeneous vector bundles, elliptic adjoint orbits and so forth.
An explicit classification of homogeneous quaternionic Kaehler structures by real tensors is derived and we relate this to the representation-theoretic description found by Fino. We then show how the quaternionic hyperbolic space HH(n) is characterised by admitting homogeneous structures of a particularly simple type. …
VB-groupoids define a special class of Lie groupoids which carry a compatible linear structure. In this paper, we show that their differentiable cohomology admits a refinement by considering the complex of cochains which are k-homogeneous on the linear fiber. Our main result is a Van Est theorem for such cochains. We a…
Datasets with a mixture of numerical and categorical attributes are routinely encountered in many application domains. In this work we examine an approach to clustering such datasets using homogeneity analysis. Homogeneity analysis determines a euclidean representation of the data. This can be analyzed by leveraging th…
Researchers found a spinorial representation for surfaces in 3D Lorentzian spaces.
problem Representation of surfaces in Lorentzian spaces.
method Spinorial representation approach.
result New correspondences between different types of surfaces in 3D spaces.
Formula derived for Laplace-Beltrami spectrum on homogeneous spaces.
problem Calculating the spectrum of the Laplace-Beltrami operator on homogeneous spaces.
method Formula derivation based on eigenvalues of a generalized Casimir operator and spherical representations.
result First detailed computation and investigation of the spectrum for a family of metrics on the Aloff-Wallach manifold.
Let G be a compact, semi-simple Lie group and H a maximal rank reductive subgroup. The irreducible representations of G can be constructed as spaces of harmonic spinors with respect to a Dirac operator on the homogeneous space G/H twisted by bundles associated to the irreducible, possibly projective, representations of…
Study on metrics and eigenvalues for compact homogeneous spaces.
problem Estimate the Laplace eigenvalue for compact homogeneous Riemannian manifolds.
method Investigate the functional for compact homogeneous spaces .
result Prove the existence of an upper bound for the mentioned functional for all compact homogeneous spaces with multiplicity-free isotropy representation.
Study homogeneous Lorentzian manifolds under reductive Lie groups, reducing descriptions to semisimple groups.
problem Characterize homogeneous Lorentzian manifolds under reductive Lie groups.
method Analyze manifolds for connected reductive Lie groups and reductive subgroup ; focus on totally reducible isotropy representations.
result Homogeneous Lorentzian manifolds reduce to semisimple Lie groups, and are reductive.
Using representations of Clifford algebras we construct indecomposable singular Riemannian foliations on round spheres, most of which are non-homogeneous. This generalizes the construction of non-homogeneous isoparametric hypersurfaces due to by Ferus, Karcher and Munzner.
We give an elementary introduction to our papers relating the geometry of rational homogeneous varieties to representation theory. We also describe related work and recent progress.
Classifies invariant spinors on nine sphere types.
problem Classifying invariant spinors on homogeneous spheres.
method Using spin representation and exterior forms, classify and describe invariant spinors.
result Determine dimensions and explicit descriptions of invariant spinors.
In this paper, we provide a systematic and constructive description of Vaisman structures on certain principal elliptic bundles over complex flag manifolds. From this description we explicitly classify homogeneous l.c.K. structures on compact homogeneous Hermitian manifolds using elements of representation theory of co…
Homogenized Transformersmath.PR
Study on deep multi-head self-attention dynamics, proving homogenized limits under specific scalings.
problem Understanding the behavior of deep multi-head self-attention models as depth increases.
method Random model of deep multi-head self-attention, viewing depth as time, and analyzing the residual stream as a particle system.
result Homogenized limit of the dynamics, leading to deterministic or stochastic behavior depending on scaling, with implications for representation collapse.
The Lagrangian representation of multi-Hamiltonian PDEs has been introduced by Y. Nutku and one of us (MVP). In this paper we focus on systems which are (at least) bi-Hamiltonian by a pair , , where is a hydrodynamic-type Hamiltonian operator. We prove that finding the Lagrangian representation is equiv…
Extends functions on symmetric spaces to analytic functions.
problem Extending functions on symmetric spaces to analytic functions.
method Harmonic analysis on symmetric spaces and representation theory of groups.
result Proves Whitney type extension theorems for symmetric spaces.
We consider the Ricci flow equation for invariant metrics on compact and connected homogeneous spaces whose isotropy representation decomposes into two irreducible inequivalent summands. By studying the corresponding dynamical system, we completely describe the behaviour of the homogeneous Ricci flow on this kind of sp…
Researchers compute the ν-invariant for specific G2-structures on Aloff-Wallach spaces.
problem Computing the ν-invariant for G2-structures on Aloff-Wallach spaces.
method Using Goette's formulas for η-invariants of homogeneous spaces, derived an explicit expression for ν.
result For the nearly-parallel G2-structures φ± on Nk,l, the ν-invariant is ν(φ±) = ±41.
Representations of -algebras are realized on section spaces of holomorphic homogeneous vector bundles. The corresponding section spaces are investigated by means of a new notion of reproducing kernel, suitable for dealing with involutive diffeomorphisms defined on the base spaces of the bundles. Applications of th…
Geometric study of thermodynamics using cotangent bundles.
problem Formulating classical thermodynamics using geometric structures.
method Contact geometry on cotangent bundles, homogeneous coordinates for intensive variables.
result Geometric formulation of thermodynamics with homogeneity properties.
Domain adaptation leverages the knowledge in one domain - the source domain - to improve learning efficiency in another domain - the target domain. Existing heterogeneous domain adaptation research is relatively well-progressed, but only in situations where the target domain contains at least a few labeled instances. I…
We describe smooth compactifications of certain families of reductive homogeneous spaces such as group manifolds for classical Lie groups, or pseudo-Riemannian analogues of real hyperbolic spaces and their complex and quaternionic counterparts. We deduce compactifications of Clifford-Klein forms of these homogeneous sp…
Study Einstein metrics on aligned homogeneous spaces with maximal third Betti number.
problem Existence and classification of Einstein metrics on specific homogeneous spaces.
method Analysis of isotropy representation and computation of Ricci curvature.
result Computation of Ricci curvature formulas for aligned homogeneous spaces.
The paper studies geodesic orbit properties in Finsler spaces.
problem Investigating geodesic orbit properties in homogeneous Finsler spaces.
method Introduced metric operator and defined standard homogeneous Finsler metrics.
result Classified homogeneous manifolds with specific geodesic orbit properties.
The paper proves rigidity theorems for forms on reductive symmetric spaces.
problem Local rigidity of forms on reductive symmetric spaces under representations of discrete groups.
method General local rigidity theorem for pull-backs of homogeneous forms, reinterpretation of old results.
result Volume of closed manifolds is constant under deformation of -structure.
We give an overview of progress on homogeneous Einstein metrics on large classes of homogeneous manifolds, such as generalized flag manifolds and Stiefel manifolds. The main difference between these two classes of homogeneous spaces is that their isotropy representation does not contain/contain equivalent summands. We …
We show that simply connected Riemannian homogeneous spaces of compact semisimple Lie groups with polar isotropy actions are symmetric, generalizing results of Fabio Podesta and the third named author. Without assuming compactness, we give a classification of Riemannian homogeneous spaces of semisimple Lie groups whose…
Analytic torsion expansions for symmetric and complex homogeneous spaces.
problem Calculating the full asymptotic expansion of analytic torsion for various spaces.
method Explicit calculation and comparison with existing results.
result Explicit full asymptotic expansions for symmetric and complex homogeneous spaces.
The space of -invariant metrics on a homogeneous space is in one-to-one correspondence with the set of inner products on the tangent space $\fr{m}\cong T_{\it o}(G/H)$, which are invariant under the isotropy representation. When all the isotropy summands are inequivalent to each other, then the metric is calle…
Sharpness of actions on reductive homogeneous spaces proven for various groups.
problem Proving proper and cocompact actions on reductive homogeneous spaces.
method Using quasi-isometric embedding and Anosov representations.
result Characterization and proof of non-compactness for certain homogeneous spaces.
This paper develops a novel analytically tractable Neumann series of Bessel functions representation for pricing (and hedging) European-style double barrier knock-out options, which can be applied to the whole class of one-dimensional time-homogeneous diffusions even for the cases where the corresponding transition den…
Motivated by Felix Klein's notion that geometry is governed by its group of symmetry transformations, Charles Ehresmann initiated the study of geometric structures on topological spaces locally modeled on a homogeneous space of a Lie group. These locally homogeneous spaces later formed the context of Thurston's 3-dimen…
We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating function for the whole sequence of heat invariants. We argue that the obtained formal s…
We establish several characterizations of Anosov representations of word hyperbolic groups into real reductive Lie groups, in terms of a Cartan projection or Lyapunov projection of the Lie group. Using a properness criterion of Benoist and Kobayashi, we derive applications to proper actions on homogeneous spaces of red…
For a compact homogeneous space , we study the problem of existence of -invariant Riemannian metrics such that each eigenspace of the Laplacian is a real irreducible representation of . We prove that the normal metric of a compact irreducible symmetric space has this property only in rank one. Furthermore, w…
Abstract: Review and definitions of generalised spin structures, their connections, and symmetry algebra.
problem Understanding and characterizing generalised spin structures and their properties.
method Definitions, basic notions, connections, covariant Lie derivative, covariant Cartan calculus, symmetry algebra.
result Characterization of homogeneous generalised spin structures.
In the present work we provide a constructive method to describe contact structures on compact homogeneous contact manifolds. The main feature of our approach is to describe the Cartan-Ehresmann connection (gauge field) for principal circle bundles over complex flag manifolds by using elements of representation theory …