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.
- Athorne, C., Algebraic invariants and generalized Hirota derivatives. Phys. Lett. A 256 (1999), no. 1, 20--24. MathSciNet Review
- 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
- 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
- A. Fring and C. Korff, Non-crystallographic reduction of generalized Calogero-Moser models, J. Phys. A: Math. Gen. 39 (2006) 1115-1131
- A. Fring and C. Korff, Affine Toda field theory related to Coxeter groups of non-crystallographic type, Nucl. Phys. B 729 (2005) 361-386
- C. Korff and K.A. Seaton, Universal amplitude ratios and Coxeter geometry in the dilute A model, Nucl. Phys. B636 [FS] (2002) 435-464
- C. Korff, Colours associated to non simply-laced Lie algebras and exact S-matrices, Phys. Lett. B501 (2001) 289-296
- A. Fring and C. Korff, Colour valued scattering matrices, Phys. Lett. B477 (2000) 380-386
- 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
- O.A.Chalykh, M.V.Feigin, A.P.Veselov, Multidimensional Baker-Akhiezer Functions and Huygens' Principle, Commun. Math. Phys., 1999, 206, pp. 533-566
- 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
- M.V.Feigin, Singular operators satisfying an intertwining relation, Theor. and Math. Physics., 1999, 121, N. 2, pp.1478-1483
- 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
- M.V.Feigin, Intertwining relations for spherical parts of generalised Calogero operators, Theor. and Math. Physics, 2003, 135(1), pp. 55-69
- 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
- M.Feigin, Quasi-invariants of dihedral systems, Mathematical Notes, 2004, 76(5), pp. 776-791
- M.Feigin, Bispectrality for deformed Calogero-Moser-Sutherland systems, Journal of Nonlin. Math. Phys., 2005, V.12,sup.2, pp. 95-136