Two new equivalences found between Lie supergroups and super Harish-Chandra pairs.
problem Establishing a new equivalence between Lie supergroups and super Harish-Chandra pairs.
method Two new functors Ψ^circ and Ψ^e that construct a Lie supergroup from a super Harish-Chandra pair.
result Both Ψ^circ and Ψ^e are quasi-inverse to the natural functor Φ from Lie supergroups to super Harish-Chandra pairs.
The paper extends algebraic constructions to Z-graded manifolds and Lie algebroids.
problem Addressing algebraic constructions in groupoids, algebroids, and Z-graded manifolds. method Generalizing results of integration of N-graded Lie algebras to Z-graded case and extending to algebroids. result Extension of Harish-Chandra pairs to algebroids and examples of application.
Study bi-graded Lie algebras and their applications.
problem Properties of Z2imesZ2-graded Lie algebras. method Harish-Chandra pairs approach to Lie group-algebra correspondence.
result Examples of application in bi-graded setting.
The paper studies highest weight representations of Lie superalgebras and their geometric realizations.
problem Understanding highest weight representations of Lie superalgebras and their geometric realizations.
method Analyzes representations of Lie superalgebras and their geometric realizations on Hermitian superspaces.
result Discovers geometric realizations of highest weight representations of Lie superalgebras.
Extends Kostant's results to symmetric pairs in Clifford algebras.
problem Analyzing k-invariants in Clifford algebras of symmetric pairs. method Proves Cartan theorem, transgression theorem, Harish-Chandra isomorphism, and Clifford algebra conjecture for relative case.
result Establishes a relative transgression theorem and Harish-Chandra isomorphism for Clifford algebras.
The paper integrates DGLA to DGLG using HCPs and Hopf algebras.
problem Integrating DGLA to DGLG.
method Definition of DGLG and HCPs, use of graded Hopf algebras.
result Construction of DGLG from DGLA and vice versa.
The study proves a geometric result related to Harish-Chandra's theorem.
problem Understanding the relationship between symmetric submanifolds and Harish-Chandra's theorem.
method Analyzing maximal tori in Clifford tori within Euclidean spaces.
result A compact, intrinsically symmetric submanifold is extrinsically symmetric if and only if its maximal tori are Clifford tori.
The article discusses extensions of Harish-Chandra's admissibility theorem.
problem Restrictions of irreducible representations to non-compact subgroups.
method Representation-theoretic developments for new spectral analysis.
result Powerful methods for spectral analysis of standard locally symmetric spaces.
Defines new algebraic structures and their interrelation.
problem None explicitly stated; focuses on definitions.
method Definition of F-algebra--Rinehart pairs and super F-algebroids.
result Connection between F-algebra--Rinehart pairs and super F-algebroids established.
Harish-Chandra's volume formula shows that the volume of a flag manifold G/T, where the measure is induced by an invariant inner product on the Lie algebra of G, is determined up to a scalar by the algebraic properties of G. This article explains how to deduce Harish-Chandra's formula from Weyl's law by utilizing…
Paper proves a fixed point formula and applies it to a new proof of Harish-Chandra's character formula.
problem Proving a fixed point formula for equivariant indices of elliptic differential operators.
method Fixed point formula for proper actions by connected semisimple Lie groups on manifolds.
result New proof of Harish-Chandra's character formula for discrete series representations.
Let λ:G~→G be the non-trivial double covering of the symplectic group G=Sp(V,ω) of the symplectic vector space (V,ω) by the metaplectic group G~=Mp(V,ω). In this case, λ is also a representation of G~ on the vector space V and thus, it gives rise to the representation of $\tilde{G…
Paper calculates indices for group actions using cocycles.
problem Calculating equivariant indices for group actions.
method Construct cyclic cocycles on Harish-Chandra's Schwartz algebra, compute pairings with equivariant indices.
result Index formula completely determines equivariant indices via topological expressions.
Survey recent constructions of cyclic cocycles for Lie groups.
problem Higher index theory for proper cocompact G-actions. method Constructions of cyclic cocycles on Harish-Chandra Schwartz algebra.
result Applications to higher index theory.
We prove the finiteness of the cohomology of torsion-free lattices in a semisimple Lie group of real rank one with coefficients in the distribution vector globalization of Harish-Chandra modules. The cohomology is expressed in terms of automorphic and cusp forms. We also consider the Lie-algebra cohomology of these glo…
New invariant constructed using stable homotopy methods.
problem Constructing a new link invariant.
method Stable homotopy theory and Khovanov's method.
result A Khovanov slk-stable homotopy type constructed. Super-OT combines GANs and optimal transport for lineage tracing.
problem Lineage tracing in single-cell RNA-seq data.
method Supervised learning framework with GANs for optimal transport.
result Super-OT outperforms Waddington-OT in predicting cell differentiation outcomes.
New metric defined for bounded symmetric domains.
problem Defining a new metric for bounded symmetric domains.
method Using generalized Hilbert metric and Borel embedding.
result The new metric differs from Carathéodory and Bergman metrics except for complex hyperbolic space.
Compactifications of SL(2) groups are studied for complex and real numbers.
problem Compactification of SL(2) groups for complex and real numbers.
method Analysis of Schwartz and Harish-Chandra Schwartz spaces as relatively standard spaces of conormal functions on compact manifolds with boundary.
result Closure under convolution and other module properties follow from the structure of generalized product spaces and functorial properties of conormal functions.
New deep learning method improves 4D Flow MRI super-resolution under domain shift.
problem Domain shift in low-resolution 4D Flow MRI data.
method Distributional deep learning framework for domain generalization.
result Framework significantly outperforms traditional methods in real data applications.
Paper defines and computes a new weight system for gl_N Lie algebra.
problem Understanding the weight system of Lie algebra gl_N.
method Two approaches: Kazarian's invariant and Harish-Chandra isomorphism.
result Computes the gl_N weight system on chord diagrams.
Generalizes Kuperberg's invariant to broader algebraic structures.
problem Extending Kuperberg's invariant to a wider class of algebraic objects.
method Constructing a scalar invariant for 3-manifolds using involutory Hopf algebras in arbitrary symmetric monoidal categories with good pairs of morphisms.
result Illustrated examples of the generalized construction for specific algebraic structures.
Defines Killing (super)algebras for spin manifolds, including gauge transformations.
problem Understanding deformations of spin structures on manifolds.
method Introduces a new algebraic structure, studies its deformations using Spencer cohomology.
result Identifies subclasses of deformations and reconstructs supersymmetric backgrounds.
New construction reveals SU(2)-flavor fields in heterotic M5-brane model.
problem Tackles the emergence of SU(2)-flavor fields in heterotic M5-brane models.
method Classifies super-exceptional field content and works out interactions.
result SU(2)xU(1)-valued scalar and vector fields emerge from probe M2- and M5-branes.
It is well known that the category of real Lie supergroups is equivalent to the category of the so-called (real) Harish-Chandra pairs. That means that a Lie supergroup depends only on the underlying Lie group and its Lie superalgebra with certain compatibility conditions. More precisely, the structure sheaf of a Lie su…
Paper defines saddle points in asymmetric Dynkin games using martingale theory.
problem Tackles saddle point conditions in asymmetric Dynkin games with partial information.
method Uses martingale theory to identify super and submartingales related to equilibrium payoffs.
result Characterizes saddle point strategies in terms of equilibrium payoffs' dynamics and Doob-Meyer decompositions.
SUPER learning combines supervised and unsupervised methods for LDCT image reconstruction.
problem Low-dose CT image reconstruction challenges.
method Combines supervised and unsupervised learning methods.
result SUPER learning dramatically outperforms constituent methods.
HighRes-net enhances satellite imagery by fusing multiple low-res views.
problem Super-resolving satellite imagery for reliable monitoring of human impact.
method End-to-end deep learning approach for multi-frame super-resolution.
result HighRes-net outperformed in European Space Agency's MFSR competition.
COBRAS uses super-instances to quickly cluster data with user queries.
problem Clustering data with user-defined pairwise constraints efficiently.
method Top-down construction of super-instances, iterative refinement based on user queries.
result COBRAS produces high-quality clusterings at fast run times.
We propose a new method for studying n- and Γ-cohomology of globalizations of Harish-Chandra modules, where G=KAN is a rank one semisimple Lie group, Γ is a discrete subgroup of G and n=Lie(N). We prove a conjecture of Patterson relating the singularities of Selberg zeta functions with the Γ-cohomology of…
A formulation for a non-trivial composition of two classical gauge structures is given: Two parent gauge structures of a common base space are synthesized so as to obtain a daughter structure which is fundamental by itself. The model is based on a pair of related connections that take their values in the product space …
In this article we construct closed, isospectral, non-isometric locally symmetric manifolds. We have three main results. First, we construct arbitrarily large sets of closed, isospectral, non-isometric manifolds. Second, we show the growth of size these sets of isospectral manifolds as a function of volume is super-pol…
New method learns internal model from expert demonstrations to estimate rewards.
problem Lack of complete or good action information from expert demonstrations.
method Agent learns internal model of observations from expert state trajectories to estimate rewards.
result Successfully trains good policies from expert game-play videos.
We prove a generalization of a theorem of Borel-Harish-Chandra on closed orbits of linear actions of reductive groups. Consider a real reductive algebraic group G acting linearly and rationally on a real vector space V. G can be viewed as the real points of a complex reductive group GC which acts on $V…
Let G/K be an irreducible Hermitian symmetric spaces of compact type with the standard homogeneous complex structure. Then the real symplectic manifold (T∗(G/K),Ω) has the natural complex structure J−. We construct all G-invariant Kähler structures (J,Ω) on homogeneous domains in T∗(G/K) anticommuting wi…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency, thereby resulting in a coherent design. The popular convex compressed sensing methods…
Study shows simplicial volume is superadditive under specific conditions.
problem Understanding superadditivity of simplicial volume under gluings.
method New results in relative bounded cohomology and pairs of multicomplexes.
result Simplicial volume is superadditive for boundary connected sums and 1-handle attachments.
Study super cluster algebras from super Plücker and Ptolemy relations.
problem Developing super cluster algebra structure in super Grassmannians.
method Analyzing super Plücker and Ptolemy relations, developing super cluster structure.
result New simple form of super Plücker relations for $\Gr_{r|1}(n|1)$.
Establishes higher T-duality for super M-branes.
problem Generalizing T-duality for super p-branes.
method Super L-infinity-algebraic T-duality for super WZW-terms.
result Spherical T-duality of super M5-branes.
Revises super unitary representations by relaxing Hilbert space definition.
problem Left-regular representations of super Lie groups are not super unitary.
method Weaken super Hilbert space definition and introduce a new metric.
result Left-regular representations of all super Lie groups are super unitary.
Bayesian image reconstruction using pre-trained generative models.
problem Distribution shifts and latent variable changes in image data.
method Combining SOTA generative models with Bayes' theorem for image restoration tasks.
result Competitive performance on super-resolution and in-painting tasks without training.
The paper defines and analyzes curvature tensors on super twisted product spaces.
problem Investigating curvature tensors on super twisted product spaces.
method Defined W2-curvature tensor, computed curvature tensors and Ricci tensors, and studied curvature flatness. result Mixed Ricci-flat super twisted product semi-Riemannian manifolds can be expressed as super warped product manifolds.
Improves conditional image generation quality on ImageNet dataset.
problem Improving conditional image generation quality on ImageNet dataset.
method Projection-based discriminator modification in GANs.
result Significantly improved image generation quality on ILSVRC2012 dataset.
Unified super-symmetry and higher fluxes using super-Lie-infinity algebras.
problem Unified extended super-symmetry and higher flux densities.
method Using super-Lie-infinity algebras and their extensions and cyclifications.
result Derivation of topological T-duality laws from super-Lie-infinity structure.
The paper studies super metrics and their local isometry groups.
problem Understanding the structure of super metrics and their isometry groups.
method Deriving canonical forms, computing covering groups, and applying Rogers' Theorem.
result For certain super metrics, the simply connected covering groups are super Lie groups with conventional super Lie algebras.
Researchers create holographic super-embeddings for M5 and M2 branes.
problem No concrete examples of super-embeddings for M5 and M2 branes existed.
method Constructed explicit holographic super-embeddings of probe M5 and M2 branes into their super-AdS backgrounds.
result Explicit holographic super-embeddings of M5 and M2 branes were successfully constructed.
New geometry connects super loops to Chern character.
problem Understanding super parallel transport on quotient stacks.
method Super holonomy on loop stacks to construct Chern character.
result Global equivariant Chern character from super holonomy.
Algorithm maximizes wealth from best pairs rebalancing rule in hindsight.
problem Maximizing wealth from best pairs rebalancing rule in hindsight.
method Extends Ordentlich and Cover's max-min universal portfolio to achieve a percentage of the hindsight-optimized wealth.
result Achieves a compound-annual growth rate arbitrarily close to the best pairs rebalancing rule in hindsight.