ar X iv : m at h / 98 11 13 9 v 2 [ m at h . Q A ] 6 J ul 1 99 9 Higher - Dimensional Algebra IV : 2 - Tangles

ar X iv : m at h / 98 11 13 9 v 1 [ m at h . Q A ] 2 4 N ov 1 99 8 Higher - Dimensional Algebra IV : 2 - Tangles

Just as knots and links can be algebraically described as certain morphisms in the category of tangles in 3 dimensions, compact surfaces smoothly embedded in R4 can be described as certain 2-morphisms in the 2-category of ‘2-tangles in 4 dimensions’. Using the work of Carter, Rieger and Saito, we prove that this 2-category is the ‘free semistrict braided monoidal 2-category with duals on one un...

ar X iv : m at h / 99 11 07 4 v 1 [ m at h . Q A ] 1 1 N ov 1 99 9 CRYSTAL GRAPHS FOR BASIC REPRESENTATIONS OF THE QUANTUM AFFINE

We give a realization of crystal graphs for basic representations of the quantum affine algebra Uq(C (1) 2) in terms of new combinatorial objects called the Young walls.

ar X iv : m at h - ph / 9 91 00 13 v 1 8 O ct 1 99 9 q - deformed

ar X iv : m at h / 99 07 16 9 v 1 [ m at h . Q A ] 2 6 Ju l 1 99 9 Integrable deformations of Hamiltonian systems and q - symmetries 1

The complete integrability of the hyperbolic Gaudin Hamiltonian and other related integrable systems is shown to be easily derived by taking into account their sl(2, R) coalgebra symmetry. By using the properties induced by such a coalgebra structure, it can be proven that the introduction of any quantum deformation of the sl(2, R) algebra will provide an integrable deformation for such systems...

ar X iv : m at h / 99 07 02 0 v 1 [ m at h . A G ] 3 J ul 1 99 9 K 3 SURFACES WITH ORDER 11 AUTOMORPHISMS

In the present paper we describe the K3 surfaces admitting order 11 automorphisms and apply this to classify log Enriques surfaces of global index 11.