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The goal of this article is twofold. First, it presents an application of the theory of invariant convex cones of Lie algebras to the study of unitary rep-resentations of Lie supergroups. Second, it p...
Previously we gave a proof of the Feigin–Fuchs character formula for the irreducible unitary discrete series of the Virasoro algebra with 0 < c < 1.
For any finite Coxeter group W, we introduce two new objects:its cutting poset and its biHecke monoid. The cutting poset, constructed using a generalization of the notion of blocks in permutation matr...
We give an abstract construction, based on the Belavin-Polyakov-Zamolodchikov equations, of a family of vertex operator algebras of rank 26 associated to the modified regular representations of the V...
We investigate the connection between representations of posets and those of the corresponding (bound) quivers. As far as quivers are concerned, we concentrate on unitarizable representations which ar...
Recently, we put forwarded a redox molecular hypothesis involving the natural biophysical substrate of visual perception and imagery. Here, we explicitly propose that the feedback and feedforward iter...
An obstacle representation of a graph G is a set of points on the plane together with a set of polygonal obstacles that determine a visibility graph isomorphic to G. The obstacle number of G is the mi...
We construct a family of irreducible unitary representations of the loop affine group of a line (ax+b group) with central extension on the Hilbert space of square integrable functions with respect to ...
The Galois representation associated to a p-divisible group over a noetherian complete local domain with perfect residue field is described in terms of its Dieudonn´e display.
Given a pair of abelian varieties defined over a number field k and isogenous over a finite Galois extension L/k, we define a rational Artin representation of the group Gal(L/k) that shows a global re...
We define left and right kernels of representations of Hopf algebras. In the case of group algebras, left and right kernels coincide and they are the usual kernels of modules.
The Dirac wave function in a curved spacetime is usually defined as a quadruplet of scalar fields. It can alternatively be defined as a four-vector field. We describe these two representations in a c...
A. Dzhumadil'daev classified all irreducible finite dimensional representations of the simple n-Lie algebra. Using a slightly different approach, we obtain in this paper a complete classification of ...
The ageing algebra is a local dynamical symmetry of many ageing systems, far from equilibrium, and with a dynamical exponent z=2. Here, new representations for an integer dynamical exponent z=n are co...
We present a program that allows for the computation of tensor products of irreducible representations of Lie algebras A-G based on the explicit construction of weight states. This straightforward ap...

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