On quantum matrix algebras satisfying the Cayley-Hamilton-Newton identities

The Cayley-Hamilton-Newton identities which generalize both the characteristic identity and the Newton relations have been recently obtained for the algebras of the RTT-type. We extend this result to a wider class of algebras M(R,F) defined by a pair of compatible solutions of the Yang-Baxter equation. This class includes the RTT-algebras as well as the Reflection equation algebras

Generalized Density Matrix Revisited: Microscopic Approach to Collective Dynamics in Soft Spherical Nuclei

The generalized density matrix (GDM) method is used to calculate microscopically the parameters of the collective Hamiltonian. Higher order anharmonicities are obtained consistently with the lowest order results, the mean field [Hartree-Fock-Bogoliubov (HFB) equation] and the harmonic potential [quasiparticle random phase approximation (QRPA)]. The method is applied to soft spherical nuclei, where the anharmonicities are essential for restoring the stability of the system, as the harmonic potential becomes small or negative. The approach is tested in three models of increasing complexity: the Lipkin model, model with factorizable forces, and the quadrupole plus pairing model.Comment: submitted to Physical Review C on 08 May, 201

Bethe subalgebras in affine Birman--Murakami--Wenzl algebras and flat connections for q-KZ equations

Commutative sets of Jucys-Murphyelements for affine braid groups of $A^{(1)},B^{(1)},C^{(1)},D^{(1)}$ types were defined. Construction of $R$-matrix representations of the affine braid group of type $C^{(1)}$ and its distinguish commutative subgroup generated by the $C^{(1)}$-type Jucys--Murphy elements are given. We describe a general method to produce flat connections for the two-boundary quantum Knizhnik-Zamolodchikov equations as necessary conditions for Sklyanin's type transfer matrix associated with the two-boundary multicomponent Zamolodchikov algebra to be invariant under the action of the $C^{(1)}$-type Jucys--Murphy elements. We specify our general construction to the case of the Birman--Murakami--Wenzl algebras. As an application we suggest a baxterization of the Dunkl--Cherednik elements $Y's$ in the double affine Hecke algebra of type $A$

On R-matrix representations of Birman-Murakami-Wenzl algebras

We show that to every local representation of the Birman-Murakami-Wenzl algebra defined by a skew-invertible R-matrix $R\in Aut(V\otimes V)$ one can associate pairings $V\otimes V\to C$ and $V^*\otimes V^*\to C$, where V is the representation space. Further, we investigate conditions under which the corresponding quantum group is of SO or Sp type.Comment: 9 page

Modified Affine Hecke Algebras and Drinfeldians of Type A

We introduce a modified affine Hecke algebra \h{H}^{+}_{q\eta}({l}) (\h{H}_{q\eta}({l})) which depends on two deformation parameters $q$ and $\eta$. When the parameter $\eta$ is equal to zero the algebra \h{H}_{q\eta=0}(l) coincides with the usual affine Hecke algebra \h{H}_{q}(l) of type $A_{l-1}$, if the parameter q goes to 1 the algebra \h{H}^{+}_{q=1\eta}(l) is isomorphic to the degenerate affine Hecke algebra \Lm_{\eta}(l) introduced by Drinfeld. We construct a functor from a category of representations of $H_{q\eta}^{+}(l)$ into a category of representations of Drinfeldian $D_{q\eta}(sl(n+1))$ which has been introduced by the first author.Comment: 11 pages, LATEX. Contribution to Proceedings "Quantum Theory and Symmetries" (Goslar, July 18-22, 1999) (World Scientific, 2000

Higher loop corrections to a Schwinger--Dyson equation

We consider the effects of higherloop corrections to a Schwinger--Dyson equations for propagators. This is made possible by the efficiency of the methods we developed in preceding works, still using the supersymmetric Wess--Zumino model as a laboratory. We obtain the dominant contributions of the three and four loop primitive divergences at high order in perturbation theory, without the need for their full evaluations. Our main conclusion is that the asymptotic behavior of the perturbative series of the renormalization function remains unchanged, and we conjecture that this will remain the case for all finite order corrections.Comment: 12 pages, 2 imbedded TiKZ pictures. A few clarifications matching the published versio