Conjectures de Lusztig
Constant solutions of Yang-Baxter equation for sl(2) and sl(3).
Constructing canonical bases of quantized enveloping algebras.
Covariant star-products
Crystal bases for the quantum queer superalgebra
In this paper, we develop the crystal basis theory for the quantum queer superalgebra . We define the notion of crystal bases and prove the tensor product rule for -modules in the category . Our main theorem shows that every -module in the category has a unique crystal basis.
Crystal bases of Verma modules for quantum affine Lie algebras
Crystals of Fock spaces and cyclotomic rational double affine Hecke algebras
We define the -restriction and -induction functors on the category of the cyclotomic rational double affine Hecke algebras. This yields a crystal on the set of isomorphism classes of simple modules, which is isomorphic to the crystal of a Fock space.
Deformation theory via deviations
Deformed commutators on comodule algebras over coquasitriangular Hopf algebras
We construct quantum commutators on comodule algebras over coquasitriangular Hopf algebras, so that they are quantum group coinvariant and have the generalized antisymmetry and Leibniz properties. If the coquasitriangular Hopf algebra is additionally cotriangular, then the quantum commutators satisfy a generalized Jacobi identity, and turn the comodule algebra into a quantum Lie algebra. Moreover, we investigate the projective and injective dimensions of some Doi-Hopf modules over a quantum commutative...
Deformed enveloping algebras.
Degenerate series representations of the -deformed algebra .
Derivations of the algebra . (Dérivations de l'algèbre .)
Description topologique des représentations de
Développements récents sur les groupes de tresses. Applications à la topologie et à l'algèbre
Differential calculus on 'non-standard' (h-deformed) Minkowski spaces
The differential calculus on 'non-standard' h-Minkowski spaces is given. In particular it is shown that, for them, it is possible to introduce coordinates and derivatives which are simultaneously hermitian.
Dilogarithm identities for sine-Gordon and reduced sine-Gordon Y-systems.
Dirac operator on the standard Podleś quantum sphere
Using principles of quantum symmetries we derive the algebraic part of the real spectral triple data for the standard Podleś quantum sphere: equivariant representation, chiral grading γ, reality structure J and the Dirac operator D, which has bounded commutators with the elements of the algebra and satisfies the first order condition.
Dressing transformation on quantum compact groups
Drinfeld doubles via derived Hall algebras and Bridgeland's Hall algebras
Let be a finitary hereditary abelian category. We give a Hall algebra presentation of Kashaev’s theorem on the relation between Drinfeld double and Heisenberg double. As applications, we obtain realizations of the Drinfeld double Hall algebra of via its derived Hall algebra and Bridgeland’s Hall algebra of -cyclic complexes.
Dual pairs, spherical harmonics and a Capelli identity in quantum group theory