arXiv research

Revises super unitary representations by relaxing Hilbert space definition.

The local structure of 4-dimensional, conformally flat, almost $ε$-Kählerian (i.e., almost pseudo-Kählerian and almost para-Kählerian) manifolds is characterized with the help of left-regular and right-regular paraquaternionic functions. Examples of such structures are discussed.

In earlier papers we studied direct limits $(G,K) = \varinjlim (G_n,K_n)$ of two types of Gelfand pairs. The first type was that in which the $G_n/K_n$ are compact Riemannian symmetric spaces. The second type was that in which $G_n = N_n\rtimes K_n$ with $N_n$ nilpotent, in other words pairs $(G_n,K_n)$ for which $G_n/…

This paper presents a spinorial representation for SpinC manifolds in Euclidean space.

Invariants for 3-manifolds with embedded links using Hopf algebras.

We study direct limits $(G,K) = \varinjlim (G_n,K_n)$ of Gelfand pairs of the form $G_n = N_n\rtimes K_n$ with $N_n$ nilpotent, in other words pairs $(G_n,K_n)$ for which $G_n/K_n$ is a commutative nilmanifold. First, we extend the criterion of \cite{W3} for a direct limit representation to be multiplicity free. Then w…

New representation theory for closed geodesic subflows.

Proves EGF representations in specific geometric contexts.

The paper establishes isomorphisms and constructs colored versions of Lawrence representations.

Study k-positive surface group representations and their degenerations.

Develops theory of Anosov representations for Fuchsian groups, showing stability and analytical properties.

This article reviews statistical methods for learning data representations.

New representations defined for groups and graphs, with applications to stable representations.

New representation connects two link invariants.

Collar lemma proven for certain surface group representations.

Study subgroup actions on mapping class groups using Heisenberg representations.

Characterizes groups for specific types of representations into SL(d,R).

Researchers describe unitary representations of mixed braid groups.

This paper addresses law invariant coherent risk measures and their Kusuoka representations. By elaborating the existence of a minimal representation we show that every Kusuoka representation can be reduced to its minimal representation. Uniqueness -- in a sense specified in the paper -- of the risk measure's Kusuoka r…

A very popular problem on braid groups has recently been solved by Bigelow and Krammer, namely, they have found a faithful linear representation for the braid group B_n. In their papers, Bigelow and Krammer suggested that their representation is the monodromy representation of a certain fibration. Our goal in this pape…

Let S be a closed orientable surface of genus at least 2 and let G be a semisimple real algebraic group of non-compact type. We consider a class of representations from the fundamental group of S to G called positively ratioed representations. These are Anosov representations with the additional condition that certain …

Polynomial representations found in surface braid and mapping class groups.

In this paper, we introduce a study of prolongations of representations of Lie groups. We obtain a faithful (one-to-one) representation of TG where G is a finite-dimensional Lie group and TG is the tangent bundle of G, by using (not necessarily faithful) representations of G. We show that tangent functions of Lie group…

Paper addresses the disparity between sampled and mean representations in disentangled learning.

Method learns state representations without supervision for Atari games.

New $Θ$-positive representations of surface groups discovered.

Investigates latent variable models for useful generative concept representations.

New representations for surface groups expand known Anosov classes.

The paper formalizes criteria for non-spurious and disentangled representations using causal methods.

New findings on cusped Borel Anosov representations and their properties.

Characterizes Anosov reducible representations in terms of eigenvalues.

This study compares global vs local observation and action representations for DRL in RTS games.

Convex-cocompact groups in infinite hyperbolic space are deformable.

In this article we introduce order preserving representations of fundamental groups of surfaces into Lie groups with bi-invariant orders. By relating order preserving representations to weakly maximal representations, introduced in arXiv:1305.2620, we show that order preserving representations into Lie groups of Hermit…

Robots learn state representation from demonstrations.

Study local structure of knot group representations into SL(n,C).

We introduce and study a new class of representations of surface groups into Lie groups of Hermitian type, called {\em weakly maximal} representations. We prove that weakly maximal representations are discrete and injective and we describe the structure of the Zariski closure of their image. Furthermore we prove that t…

We propose a family of new representations of the braid groups on surfaces that extend linear representations of the braid groups on a disc such as the Burau representation and the Lawrence-Krammer-Bigelow representation.

New method finds Fuchsian representations dominating others in surface group representations.

ICP separates and competes feature representations to learn diverse information.

The paper proposes a model to learn disentangled representations using mutual information.

New representations of Lie algebras via monoidal category actions.

The paper studies conjugating complex representations into real ones.

This paper learns actionable representations for reinforcement learning.

This paper explores the complexity of learning representations in contextual linear bandits.

This paper improves few-shot learning by reducing sample complexity using representation learning.

New CR representations are found and shown to be redundant.

This work improves understanding of reinforcement learning state representations.