Lis 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.  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.  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.   tex-file

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

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

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

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

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

19.           (with G.F. Helminck) An analytic description of the vector constrained KP hierarchy. Commun. Math. Phys. 193 (1998), 627 -- 641.  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.  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.   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, Ṣo 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.           B�¤cklund-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 Jaap Molenaar, Onno Bokhove, Lou Ramaekers, Neboj��a Gvozdenovic, Taoufik Bakri, Claude Archer, Colin Reeves) Optimizing a closed greenhouse, Proceedings of the 58th European Study Group Mathematics with Industry, Utrecht, The Netherlands, January 29 - February 2, 2007 narcis

38.           (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)

39.           (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

40.           (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)

41.           (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)

42.           (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)

43.           (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)

44.           (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)

45.           (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)

46.           (with Alexander Orlov and Takahiro Shiota) CKP Hierarchy, Bosonic Tau Function and Bosonization Formulae SIGMA 8 (2012), 036, 28 pages ( http://www.emis.de/journals/SIGMA/2012/036/)

47.           (with Dana Balibanu) Irreducible Highest Weight Representations Of The Simple n-Lie Algebra Transformation Groups Volume 17, Number 3 (2012), 593-613, DOI: 10.1007/s00031-012-9189-2   Erratum: http://link.springer.com/article/10.1007/s00031-015-9359-0           (Old version: http://xxx.uni-augsburg.de/format/1011.1396)

48.           (with Sergey Igonin, Gianni Manno and Vladimir Trushkov) Infinite-dimensional prolongation Lie algebras and multicomponent Landau-Lifshitz systems associated with higher genus curves, Journal of Geometry and Physics (2013), pp. 1-26 http://dx.doi.org/10.1016/j.geomphys.2013.02.002 (http://xxx.uni-augsburg.de/abs/1209.2999)

49.           (with Guido Carlet) Hirota equations for the extended bigraded Toda hierarchy and the total descendent potential of CP^1 orbifolds, J. Phys. A: Math. Theor. 46 (2013) 405205. arxiv

50.           (with Henrik Aratyn) B�cklund transformations for certain rational solutions of Painlev� VI, Journal of Nonlinear Mathematical Physics Volume 20, Supplement 1, 2013, 3-16 preprint arxiv

51.           The (n,1)-Reduced DKP Hierarchy, the String Equation and W Constraints,SIGMA 10 (2014), 007, 19 pages, http://www.emis.de/journals/SIGMA/2014/007/

52.           (with Guido Carlet, Hessel Posthuma and Sergey Shadrin) Towards Lax formulation of integrable hierarchies of topological type Communications in Mathematical Physics: Volume 326, Issue 3 (2014), Page 815-849  (http://arxiv.org/abs/1201.3928)

53.           (with Alexander Orlov) Pfaffian and determinantal tau functions, Letters in Mathematical Physics, Volume 105, Issue 11, (2015) pp 1499–1531  http://link.springer.com/article/10.1007/s11005-015-0786-6  (slightly different version http://arxiv.org/abs/1404.6076 )

54.     (with Laurens Stronks and Dirk Schuricht) On Rational R-matrices with adjoint SU(n) symmetry,  Journal of Physics A: Mathematical and Theoretical Vol 49, Number 44 (2016)  
            http://dx.doi.org/10.1088/1751-8113/49/44/444001
            https://arxiv.org/abs/1606.02516

55.     (with Alexander Orlov) Character expansion of matrix integrals, 2018 J. Phys. A: Math. Theor. 51 025208   https://doi.org/10.1088/1751-8121/aa9345        https://arxiv.org/abs/1611.04577

56.     (with V.G. Kac) Equivalence of formulations of the MKP hierarchy and its polynomial tau-functions, Japanese journal of Mathematics, September 2018, Volume 13, Issue 2, pp 235–271   https://doi.org/10.1007/s11537-018-1803-1    arXiv:1801.02845

57.     (with V.G. Kac) Polynomial tau-functions of BKP and DKP hierarchies.  Journal of Mathematical Physics 60, 071702 (2019); https://doi.org/10.1063/1.5085310  ArXiv: 1811.08733
       
58. (with Sylvain Carpentier,  Alberto De Sole, Victor Kac and Daniele Valeri) p-reduced multicomponent KP hierarchy and classical W-algebras W(gl_n,p),
Communications in Mathematical Physics, (), 1-68 , DOI: 10.1007/s00220-020-03817-x , arXiv:1909.03301 

In Dutch

Havengolven, Nieuwe Wiskrant 24-4/juni 2005, 15-19

Preprints

(with N. Rozhkovskaya and V. G. Kac) Polynomial Tau-functions of the KP, BKP, and the s-Component KP Hierarchies, arXiv:2005.02665

(with V.G. Kac) Polynomial tau-functions for the multi-component KP hierarchy ArXiv: 1901.07763

(with Arthemy Kiselev) Involutive distributions of operator-valued evolutionary vector fields. II ( http://xxx.uni-augsburg.de/format/0904.1555)

(with Sergey Igonin, Gianni Manno and Vladimir Trushkov) Generalized Landau-Lifshitz systems and Lie algebras associated with higher genus curves (http://xxx.uni-augsburg.de/abs/0811.4669)

(with Arthemy Kiselev) Pre-Hamiltonian structurefor integrable nonlinear systems(http://xxx.uni-augsburg.de/abs/math-ph/0703082)

A geometrical interpretation of the constrained KP hierarchy. ( Abstract or tex-file )

Twisted Toroidal Lie Algebras ( Abstract or tex-file or PostScript-file )