2,650 research outputs found
A Quantum Analogue of the Bernstein Functor
We consider Knapp-Vogan Hecke algebras in the quantum group setting. This
allows us to produce a quantum analogue of the Bernstein functor as a first
step towards the cohomological induction for quantum groups.Comment: LaTeX2e, 16 pages; some inessential corrections have been introduce
New -Matrices for Lie Bialgebra Structures over Polynomials
For a finite dimensional simple complex Lie algebra , Lie
bialgebra structures on and were
classified by Montaner, Stolin and Zelmanov. In our paper, we provide an
explicit algorithm to produce -matrices which correspond to Lie bialgebra
structures over polynomials
Q-power function over Q-commuting variables and deformed XXX, XXZ chains
We find certain functional identities for the Gauss q-power function of a sum
of q-commuting variables. Then we use these identities to obtain two-parameter
twists of the quantum affine algebra U_q (\hat{sl}_2) and of the Yangian
Y(sl_2). We determine the corresponding deformed trigonometric and rational
quantum R-matrices, which then are used in the computation of deformed XXX and
XXZ Hamiltonians.Comment: LaTeX, 12 page
On Some Lie Bialgebra Structures on Polynomial Algebras and their Quantization
We study classical twists of Lie bialgebra structures on the polynomial
current algebra , where is a simple complex
finite-dimensional Lie algebra. We focus on the structures induced by the
so-called quasi-trigonometric solutions of the classical Yang-Baxter equation.
It turns out that quasi-trigonometric -matrices fall into classes labelled
by the vertices of the extended Dynkin diagram of . We give
complete classification of quasi-trigonometric -matrices belonging to
multiplicity free simple roots (which have coefficient 1 in the decomposition
of the maximal root). We quantize solutions corresponding to the first root of
.Comment: 41 pages, LATE
Quantum (1+1) extended Galilei algebras: from Lie bialgebras to quantum R-matrices and integrable systems
The Lie bialgebras of the (1+1) extended Galilei algebra are obtained and
classified into four multiparametric families. Their quantum deformations are
obtained, together with the corresponding deformed Casimir operators. For the
coboundary cases quantum universal R-matrices are also given. Applications of
the quantum extended Galilei algebras to classical integrable systems are
explicitly developed.Comment: 16 pages, LaTeX. A detailed description of the construction of
integrable systems is carried ou
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
Universal R operator with Jordanian deformation of conformal symmetry
The Jordanian deformation of bi-algebra structure is studied in view
of physical applications to breaking of conformal symmetry in the high energy
asymptotics of scattering. Representations are formulated in terms of
polynomials, generators in terms of differential operators. The deformed
operator with generic representations is analyzed in spectral and integral
forms.Comment: 25 pages LaTex, added reference
- …