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Intelligent perception and interaction with the world hinges on internal representations that capture its underlying structure (''disentangled'' or ''abstract'' representations). Disentangled representations serve as world models, isolating…

We are interested in the classification of left-invariant symplectic structures on Lie groups. Some classifications are known, especially in low dimensions. In this paper we establish a new approach to classify (up to automorphism and…

Creating representations of shapes that are invari-ant to isometric or almost-isometric transforma-tions has long been an area of interest in shape anal-ysis, since enforcing invariance allows the learningof more effective and robust shape…

Any sufficiently often differentiable curve in the orbit space of a compact Lie group representation can be lifted to a once differentiable curve into the representation space.

In many computer vision and shape analysis tasks, practitioners are interested in learning from the shape of the object in an image, while disregarding the object's orientation. To this end, it is valuable to define a rotation-invariant…

We prove that the discontinuity group of every locally bounded homomorphism of a Lie group into a Lie group is not only compact and connected, which is known, but is also commutative.

A fundamental problem from invariant theory is to describe the endomorphism algebra of multilinear functions on a representation V invariant under the action of a group G. According to Weyl's classic, a first main (later: fundamental)…

We construct projective unitary representations of the smooth Deligne cohomology group of a compact oriented Riemannian manifold of dimension 4k+1, generalizing positive energy representations of the loop group of the circle. We also…

We study the problem of learning disentangled representations for data across multiple domains and its applications in human retargeting. Our goal is to map an input image to an identity-invariant latent representation that captures…

We propose a novel approach to disentangle the generative factors of variation underlying a given set of observations. Our method builds upon the idea that the (unknown) low-dimensional manifold underlying the data space can be explicitly…

Doubly intractable problems occur when both the likelihood and the posterior are available only in unnormalised form, with computationally intractable normalisation constants. Bayesian inference then typically requires direct approximation…

This paper is a continuation of [5]. Using the root categories, we define the compact real forms of the complex semisimple Lie algebras, and maximal compact subgroups of the Chevalley groups over $\mathbb{C}$. In [7], Lusztig used the…

Deep generative models come with the promise to learn an explainable representation for visual objects that allows image sampling, synthesis, and selective modification. The main challenge is to learn to properly model the independent…

Contrastive learning has recently emerged as a promising approach for learning data representations that discover and disentangle the explanatory factors of the data. Previous analyses of such approaches have largely focused on individual…

We study equivariant projective compactifications of reductive groups obtained by closing the image of a group in the space of operators of a projective representation. We describe the structure and the mutual position of their orbits under…

Most existing works on disentangled representation learning are solely built upon an marginal independence assumption: all factors in disentangled representations should be statistically independent. This assumption is necessary but…

In this paper, we construct a Lagrangian submanifold of the moduli space associated to the fundamental group of a punctured Riemann surface (the space of representations of this fundamental group into a compact connected Lie group). This…

We present a Bayesian model for estimating the joint distribution of multivariate categorical data when units are nested within groups. Such data arise frequently in social science settings, for example, people living in households. The…

We study unitary representations associated to cocycles of measurable dynamical systems. Our main result establishes conditions on a cocycle, ensuring that ergodicity of the dynamical system under consideration is equivalent to…

This article discusses the modular representation theory of finite groups of Lie type from the viewpoint of Broue's abelian defect group conjecture. We discuss both the defining characteristic case, the inspiration for Alperin's weight…