Related papers: The Super Orbit Challenge
Hyperdimensional (HD) computing is a set of neurally inspired methods for obtaining high-dimensional, low-precision, distributed representations of data. These representations can be combined with simple, neurally plausible algorithms to…
We define a subset of the set of special representations of a Weyl group. This subset contains at most one representation.
We study polar orbitopes, i.e. convex hulls of orbits of a polar representation of a compact Lie group. The face structure is studied by means of the gradient momentum map and it is shown that every face is exposed and is again a polar…
Since the gauge group underlying 2+1-dimensional general relativity is non-compact, certain difficulties arise in the passage from the connection to the loop representations. It is shown that these problems can be handled by appropriately…
The special linear representation of a compact Lie group G is a kind of linear representation of compact Lie group G with special properties. It is possible to define the integral of linear representation and extend this concept to special…
By a result of Babai, with finitely many exceptions, every group $G$ admits a semi-regular poset representation with three orbits, that is, a poset $P$ with automorphism group $\textrm{Aut}(P) \simeq G$ such that the action of…
Orbit functions of a simple Lie group/Lie algebra L consist of exponential functions summed up over the Weyl group of L. They are labeled by the highest weights of irreducible finite dimensional representations of L. They are of three…
We modify the Hochschild $\phi$-map to construct central extensions of a restricted Lie algebra. Such central extension gives rise to a group scheme which leads to a geometric construction of unrestricted representations. For a classical…
In this note we motivate the definition and use of Lie algebroids by revisiting the problem of reconstructing a hypersurface in Euclidean space from infinitesimal data.
We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative…
We present a theory that produces several examples where the homotopy Lie algebra of a complex hyperplane arrangement is not finitely presented. We also present examples of hyperplane arrangements where the enveloping algebra of this Lie…
In the last decade there has been a growing interest in superoscillations in various fields of mathematics, physics and engineering. However, while in applications as optics the local oscillatory behaviour is the important property, some…
Given a Lie superalgebra \g, we introduce several variants of the representation ring, built as subrings and quotients of the ring R_{\Z_2}(\g) of virtual \g-supermodules (up to even isomorphisms). In particular, we consider the ideal…
We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is the idea of a special extension of the representation…
Superspace is considered as space of parameters of the supercoherent states defining the basis for oscillator-like unitary irreducible representations of the generalized superconformal group SU(2m,2n/2N) in the field of quaternions H. The…
When supersymmetry is spontaneously broken it will be generically non-linearly realized. A method to describe the non-linear realization of supersymmetry is with constrained superfields. We discuss the basic features of this description and…
Let $\pi$ be an unitary irreducible representation of a Lie group $G$. $\pi$ defines a moment set $I_\pi$, subset of the dual $\mathfrak g^*$ of the Lie algebra of $G$. Unfortunately, $I_\pi$ does not characterize $\pi$. However, we…
For a large class of finite-dimensional Lie superalgebras (including the classical simple ones) a Lie supergroup associated to the algebra is defined by fixing the Hopf superalgebra of functions on the supergroup. Then it is shown that on…
We survey some aspects of the pseudo-differential Weyl calculus for irreducible unitary representations of nilpotent Lie groups, ranging from the classical ideas to recently obtained results. The classical Weyl-H\"ormander calculus is…
We consider the general question of when all orbits under the unitary action of a finite group give a complex spherical design. Those orbits which have large stabilisers are then good candidates for being optimal complex spherical designs.…