By Ludvig D. Faddeev, Pierre Van Moerbeke, Franklin Lambert

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A. (2000) Transvectants, modular forms, and the Heisenberg algebra, Adv. in Appl. Math. 25(3), pp. 252–283. 9. , Eilbeck, J. , and Enolskii, V. Z. (xxxx) An S L 2 (C) covariant theort of genus 2 hyper-elliptic functions, Math. Proc. Camb. Phil. , (in press). 10. , Eilbeck, J. , and Enolskii, V. Z. (2003) Identities for classical, genus 2 ℘ functions, J. Geom. , 48, pp. 354–368. 11. Baker, H. F. (1907) Multiply Periodic Functions, CUP London. 12. Pressley, A. and Segal, G. (1986) Loop Groups, Clarendon Press, Oxford.

A. (1987) Quantization of Lie groups and Lie algebras, Math. , 1, p. 193. 2. , and Yildiz, A. (2003) Invariance quantum group of the fermionic oscillator, Europ. Phys. J. C. 27, pp. 453–455. 3. Arik, M. and Kayserilio˘glu, U. (2003) Quantum invariance groups of bosons and fermions, hep-th/0304185. 4. Arik, M. and Baykal, A. (2003) Riemannian metric of the invariance group of the fermion algebra, Gen. Relat. Gravit. 35, pp. 885–890. ALGEBRAIC HIROTA MAPS Chris Athorne Department of Mathematics, University Gardens, Glasgow, G14 9LZ Abstract 1 We give definitions of Hirota maps acting as intertwining operators for representations of S L n (C).

2000) J. Phys. A33, pp. 9065–9094, hep-th/0008071. 8. Chim, L. (1996) Int. J. Mod. Phys. A11, pp. 4491–4512, hep-th/9510008. 9. Ahn, C. and Koo, W. M. (1996) Nucl. Phys. B482, p. 675, hep-th/9606003. 10. Nepomechie, R. I. Supersymmetry in the boundary tricritical Ising field theory, preprint UMTG-234, hep-th/0203123 GEOMETRY OF DISCRETE INTEGRABILITY. THE CONSISTENCY APPROACH Alexander I. Bobenko∗ Institut f¨ur Mathematik, Fakult¨at 2, Technische Universit¨at Berlin, Strasse des 17. Juni 136, 10623 Berlin, Germany 1 ORIGIN AND MOTIVATION: DIFFERENTIAL GEOMETRY Long before the theory of solitons, geometers used integrable equations to describe various special curves, surfaces etc.