ar X iv : q - a lg / 9 60 20 33 v 1 2 7 Fe b 19 96 The multiple gamma function and its q - analogue ∗

ar X iv : q - a lg / 9 60 60 16 v 1 2 3 Ju n 19 96 LIE ALGEBRAS AND THE FOUR COLOR THEOREM DROR

We present a “reasonable” statement about Lie algebras that is equivalent to the Four Color Theorem.

ar X iv : q - a lg / 9 70 20 19 v 1 1 4 Fe b 19 97 On q - Clebsch Gordan Rules and the Spinon Character Formulas for Affine C ( 1 ) 2 Algebra

The origin of this conjecture is the coincidence of the TBA equations based on the Bethe equation for the spin chain and on the S-matrix theory. It is natural to look for a description of the space of states in terms of these particles, rather than in terms of symmetry currents. Such a particle description was first obtained for sl(2) level 1 WZW model, and generalized to higher rank and/or lev...

ar X iv : a lg - g eo m / 9 60 20 19 v 1 2 7 Fe b 19 96 FORMULAS FOR LAGRANGIAN AND ORTHOGONAL DEGENERACY LOCI ; The Q̃ - Polynomials Approach

Introduction 1. Schubert subschemes and their desingularizations. 2. Isotropic Schubert calculus and the class of the diagonal. 3. Subbundles intersecting an n-subbundle in dim > k. 4. Q̃-polynomials and their properties. 5. Divided differences and isotropic Gysin maps; orthogonality of Q̃-polynomials. 6. Single Schubert condition. 7. Two Schubert conditions. 8. An operator proof of Proposition 3...

ar X iv : q - a lg / 9 60 70 28 v 1 2 7 Ju l 1 99 6 Examples of Categorification

X iv : q - a lg / 9 60 90 16 v 1 1 7 Se p 19 96 Two parameter Deformed Multimode Oscillators and q - Symmetric States

Two types of the coherent states for two parameter deformed multi-mode oscillator system are investigated. Moreover, two parameter deformed gl(n) algebra and deformed symmetric states are constructed.