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 )
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,
, 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
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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 )