Dual canonical bases for the quantum special linear group and invariant subalgebras

A string basis is constructed for each subalgebra of invariants of the function algebra on the quantum special linear group. By analyzing the string basis for a particular subalgebra of invariants, we obtain a ``canonical basis'' for every finite dimensional irreducible $U_q({\mathfrak{sl}}(n))$-module. It is also shown that the algebra of functions on any quantum homogeneous space is generated by quantum minors.Comment: 15 page

Serre presentations of Lie superalgebras

An analogue of Serre's theorem is established for finite dimensional simple Lie superalgebras, which describes presentations in terms of Chevalley generators and Serre type relations relative to all possible choices of Borel subalgebras. The proof of the theorem is conceptually transparent; it also provides an alternative approach to Serre's theorem for ordinary Lie algebras.Comment: 45 page

Quantum supergroups and topological invariants of three - manifolds

The Reshetikhin - Turaeve approach to topological invariants of three - manifolds is generalized to quantum supergroups. A general method for constructing three - manifold invariants is developed, which requires only the study of the eigenvalues of certain central elements of the quantum supergroup in irreducible representations. To illustrate how the method works, $U_q(gl(2|1))$ at odd roots of unity is studied in detail, and the corresponding topological invariants are obtained.Comment: 22 page

Topological Invariants For Lens Spaces And Exceptional Quantum Groups

The Reshetikhin - Turaev invariants arising from the quantum groups associated with the exceptional Lie algebras $G_2$, $F_4$ and $E_8$ at odd roots of unity are constructed and explicitly computed for all the lens spaces.Comment: LaTeX 10 page

Interatomic collisions in two-dimensional and quasi-two-dimensional confinements with spin-orbit coupling

We investigate the low-energy scattering and bound states of two two-component fermionic atoms in pure two-dimensional (2D) and quasi-2D confinements with Rashba spin-orbit coupling (SOC). We find that the SOC qualitatively changes the behavior of the 2D scattering amplitude in the low-energy limit. For quasi-2D systems we obtain the analytic expression for the effective-2D scattering amplitude and the algebraic equations for the two-atom bound state energy. Based on these results, we further derive the effective 2D interaction potential between two ultracold atoms in the quasi-2D confinement with Rashba SOC. These results are crucial for the control of the 2D effective physics in quasi-2D geometry via the confinement intensity and the atomic three-dimensional scattering length.Comment: 13pages, 5 figure

China's new corporate rescue laws: perspectives and principles

This article considers the new corporate insolvency legislation that came into force in China in June 2007. This law is part of a remarkable transformation in the Chinese economy in recent years. Significant numbers of ailing state owned enterprises have been reformed and subjected to hard budgetary constraints, while the private sector has grown dramatically. Market forces play a greater role, whereas the economy was previously tightly controlled by the state. These changes, together with pressures arising from external bodies such as the European Union, led to an urgent need for the adoption of the revised insolvency law, which has at its heart corporate rescue procedures. This article considers the content of this new law, the background to it, and also assesses the prospects for its operation. In particular attention is paid to the level of scope for state interference in the operation of the law