11 research outputs found
On Uq (sl2)-actions on the Quantum Plane
To give the complete list of Uq (sl2)-actions of the quantum plane, we first obtain the structure of quantum plane automorphisms. Then we introduce some special symbolic matrices to classify the series of actions using the weights. There are uncountably many isomorphism classes of the symmetries. We give the classical limit of the above actions
Classification of Uq(sl₂)-Module Algebra Structures on the Quantum Plane
A complete list of Uq(sl₂)-module algebra structures on the quantum plane is produced and the (uncountable family of) isomorphism classes of these structures are described. The composition series of representations in question are computed. The classical limits of the Uq(sl₂)-module algebra structures are discussed
A q-Analog of the Hua Equations
A necessary condition is established for a function to be in the image of a quantum Poisson integral operator associated to the Shilov boundary of the quantum matrix ball. A quantum analogue of the Hua equations is introduced
Differential Calculi on Some Quantum Prehomogeneous Vector Spaces
This paper is devoted to study of differential calculi over quadratic
algebras, which arise in the theory of quantum bounded symmetric domains. We
prove that in the quantum case dimensions of the homogeneous components of the
graded vector spaces of k-forms are the same as in the classical case. This
result is well-known for quantum matrices.
The quadratic algebras, which we consider in the present paper, are
q-analogues of the polynomial algebras on prehomogeneous vector spaces of
commutative parabolic type. This enables us to prove that the de Rham complex
is isomorphic to the dual of a quantum analogue of the generalized
Bernstein-Gelfand-Gelfand resolution.Comment: LaTeX2e, 51 pages; changed conten