The Painlevé III equation and the Iwasawa decomposition.
The quantum duality principle
The “quantum duality principle” states that the quantization of a Lie bialgebra – via a quantum universal enveloping algebra (in short, QUEA) – also provides a quantization of the dual Lie bialgebra (through its associated formal Poisson group) – via a quantum formal series Hopf algebra (QFSHA) — and, conversely, a QFSHA associated to a Lie bialgebra (via its associated formal Poisson group) yields a QUEA for the dual Lie bialgebra as well; more in detail, there exist functors and , inverse to...
The rational qKZ equation and shifted non-symmetric Jack polynomials.
The relation between Maxwell, Dirac, and the Seiberg-Witten equations.
The spectrum of coupled random matrices.
The structure of corings with a grouplike element
Characteristic properties of corings with a grouplike element are analysed. Associated differential graded rings are studied. A correspondence between categories of comodules and flat connections is established. A generalisation of the Cuntz-Quillen theorem relating existence of connections in a module to projectivity of this module is proven.
The symmetric tensor Lichnerowicz algebra and a novel associative Fourier-Jacobi algebra.
The theory of systems with internal degrees of freedom
The Virasoro algebra and some exceptional Lie and finite groups.
The Yang-Baxter and pentagon equation
Tools for verifying classical and quantum superintegrability.
Topological quasi *-algebras and the time evolution of systems
We give here a survey of some recent results on applications of topological quasi *-algebras to the analysis of the time evolution of quantum systems with infinitely many degrees of freedom.
Towards finite-gap integration of the Inozemtsev model.
Traces dans les catégories monoïdales, dualité et catégories monoïdales fibrées
Translation-invariant noncommutative renormalization.
Triangular Lie bialgebras and matched pairs for Lie algebras of real vector fields on .
Twisted quantum doubles.
Twisted spectral triples and covariant differential calculi
Connes and Moscovici recently studied "twisted" spectral triples (A,H,D) in which the commutators [D,a] are replaced by D∘a - σ(a)∘D, where σ is a second representation of A on H. The aim of this note is to point out that this yields representations of arbitrary covariant differential calculi over Hopf algebras in the sense of Woronowicz. For compact quantum groups, H can be completed to a Hilbert space and the calculus is given by bounded operators. At the end, we discuss an explicit example of...
Two classical results in the quantum mixed case.
Two point correlation functions for a periodic box-ball system.