Department of Mathematics

List of Publications

PhD-thesis

Contragredient Lie superalgebras of finite growth.
Thesis R.U.U., May 1986.

Articles

1. (with V.G. Kac) Super boson-fermion correspondence.
   Anales de l'Institut Fourier, 37 (1987), 99 - 137.

2. A classification of contragredient Lie superalgebras of finite growth.
   Communications in Algebra 17 (1989), 1815 - 1841.

3. (with V.G. Kac) On classification of superconformal algebras.
   In ``Strings 88'' (proceedings of the conference at the University of Maryland at College Park, May 24 - 28, 1988) edited by S.J. Gates, C.R. Preitschopf, W. Siegel, World Scientific, Singapore, 77 - 106.

4. (with V.G. Kac) A super boson-fermion correspondence of type B.
   In ``Infinite Dimensional Lie Algebras and Groups'' (proceedings of the conference held at CIRM, Luminy, July 4 - 8, 1988) edited by V.G. Kac, Advanced Series in Mat. Phys. Vol. 7, World Scientific, Singapore, 369 - 406.

5. (with A.P.E. ten Kroode) Representations of the infinite matrix algebra.
   CWI Quarterly 3 (1990), 21 - 43.

6. (with A.P.E. ten Kroode) Bosonic and fermionic realizations of the affine algebra gl(n).
   Comm. Math. Phys. 137 (1991), 67 - 107.
   ( Abstract )

7. (with A.P.E. ten Kroode) Bosonic and fermionic realizations of the affine algebra so(2n).
   Comm. in Algebra 20 (1992), 3119 - 3162.
   ( Abstract )

8. (with A.P.E. ten Kroode) Level one representations of the twisted affine algebras A_n^(2) and D_n^(2).
   Acta Appl. Math. 27 (1992), 153 - 224.
   ( Abstract or tex-file

9. (with A.P.E. ten Kroode) Level one representations of the affine Lie algebra B_n^(1).
   Acta Appl. Math. 31 (1993), 1 - 73.
   ( Abstract or tex-file )

10. (with V.G. Kac) The $n$-component $KP$ hierarchy and representation theory.
    In ``Important developments in soliton theory'', eds. A.S. Fokas and V. E. Zakharov, Springer Series in Nonlinear Dynamics (1993), 302 - 343.
    (Tex-file )

11. The [n_1,n_2,...,n_s]-th reduced KP hierarchy and W_{1+\infty} constraints.
    In proceedings of the V International Conference on Mathematical Physics, String Theory and Quantum Gravity (Alushta, June 10-20 1994),Teoret. Mat. Fiz. 104 (1) (1995), 32 -- 42, Translation in Theoret. and Math. Phys. 104 (1) (1996), 783 -- 792.
    ( Abstract or tex-file )

12. KdV type hierarchies, the string equation and W_{1+\infty} constraints.
    Journal of Geometry and Physics 17 (1995), 95 - 124.
    ( Abstract or tex-file )

13. The Adler-Shiota-van Moerbeke formula for the BKP hierarchy.
    Jour. Math. Phys. 36 (1995), 4940 - 4951.
    ( Abstract or tex-file )

14. The W_{1+\infty}(gl(s))-symmetries of the s-component KP hierarchy.
    Jour. Math. Phys. 37 (1996), 2315 - 2337 (and hep-th 9411069).
    ( Abstract or tex-file )

15. The n-th reduced BKP hierarchy, the string equation and BW_{1+\infty}-constraints.
    Acta Appl. Math. 44 (1996), 185 - 206.
    ( Abstract or tex-file )

16. The vector k-constrained KP hierarchy and Sato's Grassmannian.
    Journal of Geometry and Physics 23 (1997), 83 - 96.
    ( Abstract or tex-file )

17. Schlesinger--B\"acklund transformations for the n-component KP.
    Jour. Math. Phys. 39 (1998), 2833 -- 2847.
    ( Abstract or tex-file )

18. (with V.G. Kac) The geometry of spinors and the multicomponent BKP and DKP hierarchies.
    in ``The Bispectral Problem'', eds. J. Harnad, A. Kasman CRM Proceedings and lecture Notes 14 (1998), 159 -- 202
    ( Abstract or tex-file )

19. (with G.F. Helminck) An analytic description of the vector constrained KP hierarchy.
    Commun. Math. Phys. 193 (1998), 627 -- 641
    ( Abstract or tex-file )

20. (with G.F. Helminck) Constrained and Rational Reductions of the KP hierarchy,
    in "Supersymmetry and Integrable Models", Springer Lecture Notes in Physics 502 (1998), 167 -- 182.
    ( Abstract or tex-file )

21. (with R. Martini) The construction of Frobenius manifolds from KP tau-functions.
    Commun. Math. Phys. 205 (1999) 587--616 and solv-int 9808008.
    ( Abstract or tex-file or PostScript-file )

22. (with G.F. Helminck) A geometric construction of the dual wavefunction of the n-component KP-hierarchy.
    in "Lie Theory and Its Applications in Physics III", edited by H.-D Doebner, V.K. Dobrev and J. Hilgert, World Scientific (2000), 187 -- 203. (PostScript-file)

23. (with G.F. Helminck) Darboux transformations for the KP hierarchy in the Segal-Wilson setting, Canadian Journ Math. 53 (no. 2) (2001) 278--309.
    (PostScript-file)

24. Matrix Integrals and the Geometry of Spinors.
    Journ. of Nonlinear Math. Phys. 8(2) (2001)288-310 (solv-int/9909028)
    ( Abstract or tex-file or PostScript-file )

25. Twisted GL_n Loop Group Orbit and Solutions of the WDVV Equations, Intern. Math. Research Notices 2001, vol 11 (2001), 551 -- 574.
    old version: nlin/0004021
    ( Abstract or tex-file or PostScript-file )
    

26. (with G.F. Helminck) Geometric B\"acklund--Darboux transformations for the KP hierarchy. Publ. Res. Inst. Math. Sci. 37 (2001), no. 4, 479--519.
    (PostScript-file revised and final version)

27. (with Henrik Aratyn) Integrable Structure behind WDVV Equations, Theoretical and Mathematical Physics, January 2003, Volume 134, Issue 1, pp. 14 -- 26.
    ( journal or hep-th/0111243 PostScript-file )
    

28. (with Henrik Aratyn, J.F. Gomes, A.H. Zimerman) WDVV Equations, Darboux-Egoroff Metric and the Dressing Method
    in electronic proceedinges ( JHEP) of the Workshop on Integrable Theories, Solitons and Duality, 1-6 July 2002, São Paulo, Brazil
    ( Abstract or Pdf-file )
    

29. (with V.G. Kac) The $n$-component $KP$ hierarchy and representation theory.
    Jour. Math. Phys. Volume 44, Issue 8, pp. 3245-3293 (2003)
    Pdf-file
    

30. (with Henrik Aratyn) Solutions of the WDVV Equations and Integrable Hierarchies of KP type, Commun. Math. Phys. 239 (2003), pp. 155 - 182
    Pdf-file
    ( or hep-th PostScript-file )
    

31. (with G.F. Helminck) Elementary Darboux transformations of the n-component KP-hierarchy, Int. J. Diff. Eq Appl. Vol.7, no 4 (2003) 375-413
    

32. Bäcklund-Darboux Transformations for the Coupled KP Hierarchy.
    Journal of Physics A: Mathematical and General, volume 37, issue 15 (2004), 4395 - 4405

33. (with Henrik Aratyn) The symplectic Kadomtsev-Petviashvili hierarchy and rational solutions of Painlev\'e VI, Ann. Inst. Fourier 55 (6) (2005), 1871-1903
    (see also Abstract/ps/pdf-files nlin.SI/0406038 )

34. (with Henrik Aratyn) The CKP hierarchy and the WDVV prepotential, in:
    Bilinear Integrable Systems: from Classical to Quantum, Continuous to Discrete, Series: NATO Science Series II: Mathematics, Physics and Chemistry , Vol. 201 Faddeev, Ludwig; Van Moerbeke, Pierre; Lambert, Franklin (Eds.), 2006, p. 1 - 11
    ( Abstract or tex-file or Pdf-file )
    

35. Baecklund transformations for new integrable hierarchies related to the polynomial Lie algebra gl^{(n)}_\infty, Journal of Geometry and Physics 57 (2007) 435-447
    (see: science direct info page)

36. (with Henrik Aratyn) Clifford algebra derivations of tau functions for two-dimensional integrable models with positive and negative flows, SIGMA 3 (2007), 020, 29 pages

37. (with Henrik Aratyn) Solutions of the Painleve VI Equation from Reduction of Integrable Hierarchy in a Grassmannian Approach,
    International Mathematics Research Notices 2008 2008: rnn080-41,
    journals pdf-file
    (http://xxx.uni-augsburg.de/abs/0804.0785, slightly different version)

38. (with Alexander Yu. Orlov) Random turn walk on a half line with creation of particles at the origin,
    Physics Letters A Volume 373, Issue 31, 20 July 2009, Pages 2675-2681, article; larger version: http://xxx.uni-augsburg.de/abs/0801.0066

39. (with Arthemy Kiselev) A family of second Lie algebra structures for symmetries of dispersionless Boussinesq system,
    J. Phys. A: Math. Theor. 42 404011 (8pp) doi: 10.1088/1751-8113/42/40/404011 article,
    ( http://xxx.uni-augsburg.de/abs/0903.1214)

40. (with Arthemy Kiselev) A geometric derivation of KdV-type hierarchies from root systems
    in: Proc. 4th int. Workshop "Group Analysis of Differential Equations and Integrable Systems.", 87-106 (2009).
    ( http://xxx.uni-augsburg.de/abs/0901.4866)

41. (with Arthemy Kiselev) Symmetry algebras of Lagrangian Liouville-type systems
    Theoretical and Mathematical Physics, 162(2): 149-162 (2010)
    ( http://xxx.uni-augsburg.de/abs/0902.3624)

42. (with Evgeny Feigin and Sergey Shadrin) Givental symmetries of Frobenius manifolds and multi-component KP tau-functions,
    Advances in Mathematics 224 (2010) 1031–1056
    ( http://xxx.uni-augsburg.de/format/0905.0795)

43. (with Arthemy Kiselev) Variational Lie algebroids and homological evolutionary vector fields
    Theoretical and mathematical physics, 167(3):772-784 (2011)
    ( http://igitur-archive.library.uu.nl/math/2011-0210-200333/UUindex.html)

44. (with John Harnad and Alexander Orlov) Multiple sums and integrals as neutral BKP tau functions
    Theoretical and Mathematical Physics, 168(1): 951–962 (2011)
    ( http://xxx.uni-augsburg.de/format/1101.4216)

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