On the degenerate multiplicity of the loop algebra for the 6V transfer matrix at roots of unity.
On the geometry of complex Grassmann manifold, its noncompact dual and coherent states.
On the mass spectrum of Higgs particles
On the mini-superambitwistor space and super-Yang-Mills theory.
On the principle of stability of invariance of physical systems
On the problem of classifying simple compact quantum groups
We review the notion of simple compact quantum groups and examples, and discuss the problem of construction and classification of simple compact quantum groups.
On the set-theoretical Yang-Baxter equation.
On the supergroup and its superfield representations
On the uniqueness of the -dimensional supertorus associated to a nontrivial representation of its underlying 2-torus, and having nontrivial odd brackets.
On two possible constructions of the quantum semigroup of all quantum permutations of an infinite countable set
Two different models for a Hopf-von Neumann algebra of bounded functions on the quantum semigroup of all (quantum) permutations of infinitely many elements are proposed, one based on projective limits of enveloping von Neumann algebras related to finite quantum permutation groups, and the second on a universal property with respect to infinite magic unitaries.
On wave functions in quantum mechanics
On wave functions in quantum mechanics. Part 3. A theory of quantum mechanics where wave functions are defined by means of surely fundamental observables
One-dimensional vertex models associated with a class of Yangian invariant Haldane-Shastry like spin chains.
Optimal Holomorphic Hypercontractivity for CAR Algebras
We present a new proof of Janson’s strong hypercontractivity inequality for the Ornstein-Uhlenbeck semigroup in holomorphic algebras associated with CAR (canonical anticommutation relations) algebras. In the one generator case we calculate optimal bounds for t such that is a contraction as a map for arbitrary p ≥ 2. We also prove a logarithmic Sobolev inequality.
Ordering of energy levels for extended Hubbard chain.
Para-Grassmann variables and coherent states.
Physique et mathématique
Poisson Lie groups and their relations to quantum groups
The notion of Poisson Lie group (sometimes called Poisson Drinfel'd group) was first introduced by Drinfel'd [1] and studied by Semenov-Tian-Shansky [7] to understand the Hamiltonian structure of the group of dressing transformations of a completely integrable system. The Poisson Lie groups play an important role in the mathematical theories of quantization and in nonlinear integrable equations. The aim of our lecture is to point out the naturality of this notion and to present basic facts about...
Polarization and Unitary Representations of Solvable Lie Groups.
Power of a determinant with two physical applications.