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There are good reasons to believe that we are classical algorithms run on (effectively) classical machines. However, the fact that a physical state of a system in a universe described by a classical d...
We use semigroup theory to describe the group of automorphisms of some semigroups of interest in holomorphic dynamical systems. We show,with some examples, that representation theory of semigroups is ...
Matrices of locally analytic functions in two variables correspond to the maximal Cohen-Macaulay modules over plane curve singularities and to the local determinantal representations.
The equation ∂2 ∂z∂¯z log(s2) = |Q|2s−4 + s2 (1.1) is satisfied by the conformally flat metric s2|dz|2 of a minimal Lagrangian surface in the complex hyperbolic plane CH2,...
For G an arbitrary unimodular Lie group, we construct strongly continuous unitary representations of G in the Bergman space of a naturally constructed strongly pseudoconvex neighborhood of the complex...
We give a unified construction of the minimal representation of a finite cover G of the conformal group of a (non necessarily euclidean) Jordan algebra V . This representation is realized on the L2-sp...
In the first part of this paper, we prove the existence of torsion free covers in the category of representations of quivers, (Q,R-Mod),for a wide class of quivers included in the class of the so-cal...
With the help of a useful mathematical tool, the polar decomposition of closed operators, and a simple observation, i.e. the unique relation between tensor-product states and compact operators, we man...
Governed by locality, we explore a connection between unitary braid group representations associated to a unitary R-matrix and to a simple object in a unitary braided fusion category.
We give a complete description of the category of smooth complex representations of the multiplicative group of a central simple algebra over a locally compact nonarchimedean local field. More precise...
Let k be a field and  the n-Kronecker algebra, this is the path algebra of the quiver with 2 vertices, a source and a sink, and n arrows from the source to the sink. It is wellknown that the dimensi...
We construct via generators and relations, generalized Weil representations for analogues of classical SL(2, k), k a field, over involutive base rings (A, ∗). This family of groups covers diff...
We discuss the category I of level zero integrable representations of loop algebras and their generalizations. The category is not semisimple and so one is interested in its homological properties.
Lowest weight modules, in particular, Verma modules over the N = 1, 2 super Schr¨odinger algebras in (1+1) dimensional spacetime are investigated. The reducibility of the Verma modules is analyzed v...
We consider finite W-algebras U(g, e) associated to even multiplicity nilpotent elements in classical Lie algebras. We give a classification of finite dimensional irreducible U(g, e)-modules with inte...

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