Square integrability of group representations on homogeneous spaces. I. Reproducing triples and frames
Statistics and quantum group symmetries
Using 'twisted' realizations of the symmetric groups, we show that Bose and Fermi statistics are compatible with transformations generated by compact quantum groups of Drinfel'd type.
Strange phenomena related to ordering problems in quantizations.
Structure fractals and para-quaternionic geometry
It is well known that starting with real structure, the Cayley-Dickson process gives complex, quaternionic, and octonionic (Cayley) structures related to the Adolf Hurwitz composition formula for dimensions p = 2, 4 and 8, respectively, but the procedure fails for p = 16 in the sense that the composition formula involves no more a triple of quadratic forms of the same dimension; the other two dimensions are n = 27. Instead, Ławrynowicz and Suzuki (2001) have considered graded fractal bundles of...
Structure theory for second order 2D superintegrable systems with 1-parameter potentials.
nonstandard bases: case of mutually unbiased bases.
Subgroups of the group of generalized Lorentz transformations and their geometric invariants.
Superconnections: an interpretation of the standard model.
Superintegrable oscillator and Kepler systems on spaces of nonconstant curvature via the Stäckel transform.
Supersymmetric extension of non-Hermitian Hamiltonian and supercoherent states.
Supersymmetric representations and integrable fermionic extensions of the Burgers and Boussinesq equations.
Supersymmetry of affine Toda models as fermionic symmetry flows of the extended mkdv hierarchy.
Sur un nouveau groupe de symétrie de la mécanique quantique relativiste
SUSY quantum Hall effect on non-anti-commutative geometry.
Symmetric quantum Weyl algebras
We study the symmetric powers of four algebras: -oscillator algebra, -Weyl algebra, -Weyl algebra and . We provide explicit formulae as well as combinatorial interpretation for the normal coordinates of products of arbitrary elements in the above algebras.
Symmetries of an extended Hubbard Model
The Hamiltonian for an extended Hubbard model with phonons as introduced by A. Montorsi and M. Rasetti is considered on a D-dimensional lattice. The symmetries of the model are studied in various cases. It is shown that for a certain choice of the parameters a superconducting holds as a true quantum symmetry, but only for D=1.
Symmetries of spin Calogero models.
Symmetries, variational principles, and quantum dynamics.
Symmetry breaking via internal geometry.
Symplectic twistor operator and its solution space on
We introduce the symplectic twistor operator in symplectic spin geometry of real dimension two, as a symplectic analogue of the Dolbeault operator in complex spin geometry of complex dimension 1. Based on the techniques of the metaplectic Howe duality and algebraic Weyl algebra, we compute the space of its solutions on .