Algebra and geometry

Several of our research areas have algebraic and geometric aspects, in particular the connections between discrete maps and the geometry of surfaces, integrable lattices of geometric invariants associated with differential systems and the role of generalized Hirota derivatives in the representation theory of sl(n,C). One of the topics is algebraic structures arising in integrable systems based on Coxeter geometry, this includes the study of generalized Calogero-Moser systems, affine Toda field theories and their quantum conserved quantities.

1. Athorne, C., Algebraic invariants and generalized Hirota derivatives. Phys. Lett. A 256 (1999), no. 1, 20--24. MathSciNet Review
2. Nimmo, J. J. C.; Schief, W. K. An integrable discretization of a $(2+1)$-dimensional sine-Gordon equation. Stud. Appl. Math. 100 (1998), no. 3, 295--309. MathSciNet Review
3. Athorne, C. A $\bold Z\sp 2\times\bold R\sp 3$ Toda system. Phys. Lett. A 206 (1995), no. 3-4, 162--166. MathSciNet Review
4. A. Fring and C. Korff, Non-crystallographic reduction of generalized Calogero-Moser models, J. Phys. A: Math. Gen. 39 (2006) 1115-1131
5. A. Fring and C. Korff, Affine Toda field theory related to Coxeter groups of non-crystallographic type, Nucl. Phys. B 729 (2005) 361-386
6. C. Korff and K.A. Seaton, Universal amplitude ratios and Coxeter geometry in the dilute A model, Nucl. Phys. B636 [FS] (2002) 435-464
7. C. Korff, Colours associated to non simply-laced Lie algebras and exact S-matrices, Phys. Lett. B501 (2001) 289-296
8. A. Fring and C. Korff, Colour valued scattering matrices, Phys. Lett. B477 (2000) 380-386
9. A. Fring, C.Korff and B.J. Schulz, On the universal representation of the scattering matrix of affine Toda field theory, Nucl. Phys. B567 (2000) 409-453
10. O.A.Chalykh, M.V.Feigin, A.P.Veselov, Multidimensional Baker-Akhiezer Functions and Huygens' Principle, Commun. Math. Phys., 1999, 206, pp. 533-566
11. O.A.Chalykh, M.V.Feigin, A.P.Veselov, New integrable generalizations of Calogero-Moser quantum problem, J. Math. Phys., 1998, 39 (2), pp. 695-703
12. M.V.Feigin, Singular operators satisfying an intertwining relation, Theor. and Math. Physics., 1999, 121, N. 2, pp.1478-1483
13. M.V.Feigin, A.P.Veselov, Quasi-invariants of Coxeter groups and m-harmonic polynomials, Intern. Math. Res. Notices, 2002, N. 10, pp. 521-545
14. M.V.Feigin, Intertwining relations for spherical parts of generalised Calogero operators, Theor. and Math. Physics, 2003, 135(1), pp. 55-69
15. M. Feigin, A.P.Veselov, Quasi-invariants and quantum integrals of the deformed Calogero-Moser systems, Intern. Math. Res. Notices, 2003, V. 46, pp. 2487-2511
16. M.Feigin, Quasi-invariants of dihedral systems, Mathematical Notes, 2004, 76(5), pp. 776-791
17. M.Feigin, Bispectrality for deformed Calogero-Moser-Sutherland systems, Journal of Nonlin. Math. Phys., 2005, V.12,sup.2, pp. 95-136