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Volumn 44, Issue 8, 2003, Pages 3245-3293

The n-component KP hierarchy and representation theory

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EID: 0041728683     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1590055     Document Type: Article
Times cited : (133)

References (55)
  • 1
    • 0002004721 scopus 로고
    • Solitons, nonlinear evolution equations and inverse scattering
    • Cambridge University Press, Cambridge
    • Ablowitz, M. J. and Clarkson, P. A., Solitons, nonlinear evolution equations and inverse scattering, London Math. Soc. Lecture Note Series 149 (Cambridge University Press, Cambridge, 1991).
    • (1991) London Math. Soc. Lecture Note Series , vol.149
    • Ablowitz, M.J.1    Clarkson, P.A.2
  • 2
    • 0007017126 scopus 로고
    • ∞algebra to its central extension: A τ-function approach
    • ∞algebra to its central extension: a τ-function approach," Phys. Lett. A 194, 33-34 (1994).
    • (1994) Phys. Lett. A , vol.194 , pp. 33-34
    • Adler, M.1    Shiota, T.2    Van Moerbeke, P.3
  • 3
    • 0005195571 scopus 로고
    • A Lax representation of the vertex operator and the central extension
    • Adler, M., Shiota, T., and van Moerbeke, P., "A Lax representation of the vertex operator and the central extension," Commun. Math. Phys. 171, 547-588 (1995).
    • (1995) Commun. Math. Phys. , vol.171 , pp. 547-588
    • Adler, M.1    Shiota, T.2    Van Moerbeke, P.3
  • 5
    • 84972560172 scopus 로고
    • Partitions, vertex operator constructions and multi-component KP equations
    • Bergvelt, M. J. and ten Kroode, A. P. E., "Partitions, vertex operator constructions and multi-component KP equations," Pac. J. Math. 171, 23-88 (1995).
    • (1995) Pac. J. Math. , vol.171 , pp. 23-88
    • Bergvelt, M.J.1    Ten Kroode, A.P.E.2
  • 6
    • 45549119495 scopus 로고
    • Scattering of localized solitons in the plane
    • Boiti, M., Leon, J., Martina, L., and Pempinelli, F., "Scattering of localized solitons in the plane," Phys. Lett. A 132, 432-439 (1988).
    • (1988) Phys. Lett. A , vol.132 , pp. 432-439
    • Boiti, M.1    Leon, J.2    Martina, L.3    Pempinelli, F.4
  • 7
    • 0001519224 scopus 로고
    • Operator approach to the Kadomtsev-Petviashvili equation. Transformation groups for soliton equations. III
    • Date, E., Jimbo, M., Kashiwara, M., and Miwa, T., "Operator approach to the Kadomtsev-Petviashvili equation. Transformation groups for soliton equations. III," J. Phys. Soc. Jpn. 50, 3806-3812 (1981).
    • (1981) J. Phys. Soc. Jpn. , vol.50 , pp. 3806-3812
    • Date, E.1    Jimbo, M.2    Kashiwara, M.3    Miwa, T.4
  • 8
    • 84996377707 scopus 로고
    • Transformation groups for soliton equations. Euclidean Lie algebras and reduction of the KP hierarchy
    • Date, E., Jimbo, M., Kashiwara, M., and Miwa, T., "Transformation groups for soliton equations. Euclidean Lie algebras and reduction of the KP hierarchy," Publ. Res. Inst. Math. Sci. 18, 1077-1110 (1982).
    • (1982) Publ. Res. Inst. Math. Sci. , vol.18 , pp. 1077-1110
    • Date, E.1    Jimbo, M.2    Kashiwara, M.3    Miwa, T.4
  • 10
    • 0041564630 scopus 로고
    • On Segal-Wilson's definition of the τ-function and hierarchies of AKNS-D and mcKP
    • Integrable Systems (Luminy, 1991) (Birkhuser, Boston)
    • Dickey, L. A., "On Segal-Wilson's definition of the τ-function and hierarchies of AKNS-D and mcKP," in Integrable Systems (Luminy, 1991), pp. 147-161, Progress in Mathematics, Vol 115 (Birkhuser, Boston, 1993).
    • (1993) Progress in Mathematics , vol.115 , pp. 147-161
    • Dickey, L.A.1
  • 11
    • 0042566788 scopus 로고
    • Completely integrable Hamiltonian systems related to matrix operators, and abelian manifolds
    • Dubrovin, B. A., "Completely integrable Hamiltonian systems related to matrix operators, and abelian manifolds," Funct. Anal. Appl. 11, 28-41 (1977).
    • (1977) Funct. Anal. Appl. , vol.11 , pp. 28-41
    • Dubrovin, B.A.1
  • 12
    • 0347427534 scopus 로고
    • Integrable systems in lopological field theory
    • Dubrovin, B. A., "Integrable systems in lopological field theory," Nucl. Phys. B 379, 627-689 (1992).
    • (1992) Nucl. Phys. B , vol.379 , pp. 627-689
    • Dubrovin, B.A.1
  • 13
    • 0042566761 scopus 로고
    • Integrable systems and classification of 2-dimensional topological field theories
    • Integrable Systems (Luminy, 1991) (Birkhäuser, Boston)
    • Dubrovin, B. A., "Integrable systems and classification of 2-dimensional topological field theories," in Integrable Systems (Luminy, 1991). Progress in Mathematics, Vol. 115 (Birkhäuser, Boston, 1993), pp. 613-359.
    • (1993) Progress in Mathematics , vol.115 , pp. 613-359
    • Dubrovin, B.A.1
  • 14
    • 0000644797 scopus 로고    scopus 로고
    • Geometry of 2D topological field theories
    • Integrable systems and quantum groups (Montecatini Terme, 1993) (Springer, Berlin)
    • Dubrovin, B. A., "Geometry of 2D topological field theories," in Integrable systems and quantum groups (Montecatini Terme, 1993), Lecture Notes in Math., Vol. 1620 (Springer, Berlin, 1996), pp. 120-348.
    • (1996) Lecture Notes in Math. , vol.1620 , pp. 120-348
    • Dubrovin, B.A.1
  • 15
    • 0032276702 scopus 로고    scopus 로고
    • Bi-Hamiltonian hierarchies in 2D topological field theory at one-loop approximation
    • Dubrovin, B. A. and Zhang, Y.-J., "Bi-Hamiltonian hierarchies in 2D topological field theory at one-loop approximation," Commun. Math. Phys. 198, 311-361 (1998).
    • (1998) Commun. Math. Phys. , vol.198 , pp. 311-361
    • Dubrovin, B.A.1    Zhang, Y.-J.2
  • 16
    • 0002630015 scopus 로고
    • Basic representations of affine Lie algebras and dual resonance models
    • Frenkel, I. B. and Kac, V. G., "Basic representations of affine Lie algebras and dual resonance models," Invent. Math. 62, 23-66 (1980).
    • (1980) Invent. Math. , vol.62 , pp. 23-66
    • Frenkel, I.B.1    Kac, V.G.2
  • 18
    • 0039587886 scopus 로고
    • Recursion operators and bi-Hamiltonian structures in multidimensions. H
    • Fokas, A. S. and Santini, P. M., "Recursion operators and bi-Hamiltonian structures in multidimensions. H.," Commun. Math. Phys. 116, 449-474 (1988).
    • (1988) Commun. Math. Phys. , vol.116 , pp. 449-474
    • Fokas, A.S.1    Santini, P.M.2
  • 19
    • 4244193388 scopus 로고
    • Dromions and boundary value problem for the Davey-Stewartson 1 equation
    • Fokas, A. S. and Santini, P. M., "Dromions and boundary value problem for the Davey-Stewartson 1 equation," Physica D 44, 99-130 (1990).
    • (1990) Physica D , vol.44 , pp. 99-130
    • Fokas, A.S.1    Santini, P.M.2
  • 20
    • 0011095251 scopus 로고
    • Some identities for abelian integrals
    • Gunning, R. C., "Some identities for abelian integrals," Am. J. Math. 108, 39-74 (1986).
    • (1986) Am. J. Math. , vol.108 , pp. 39-74
    • Gunning, R.C.1
  • 22
    • 0000782741 scopus 로고
    • Multidromion solutions of the Davey-Stewartson equation
    • Hietarinta, J. and Hirota, R., "Multidromion solutions of the Davey-Stewartson equation," Phys. Lett. A 145, 237-244 (1990).
    • (1990) Phys. Lett. A , vol.145 , pp. 237-244
    • Hietarinta, J.1    Hirota, R.2
  • 23
    • 0002464716 scopus 로고
    • Direct method in soliton theory
    • edited by R. K. Bullough and P. J. Caudrey (Springer Verlag, New York)
    • Hirota, R., "Direct method in soliton theory," in Solitons, edited by R. K. Bullough and P. J. Caudrey (Springer Verlag, New York, 1980).
    • (1980) Solitons
    • Hirota, R.1
  • 24
    • 85008279103 scopus 로고
    • Solitons and infinite dimensional Lie algebras
    • Jimbo, M. and Miwa, T., "Solitons and infinite dimensional Lie algebras," Publ. Res. Inst. Math. Sci. 19, 943-1001 (1983).
    • (1983) Publ. Res. Inst. Math. Sci. , vol.19 , pp. 943-1001
    • Jimbo, M.1    Miwa, T.2
  • 25
    • 0003273558 scopus 로고
    • Infinite dimensional lie algebras
    • Brikhäuser, Boston
    • Kac, V. G., "Infinite Dimensional Lie Algebras," Progress in Math., Vol. 44 (Brikhäuser, Boston, 1983); 2nd ed. (Cambridge University Press, Cambridge, 1985); 3rd ed. (Cambridge University Press, Cambridge 1990).
    • (1983) Progress in Math. , vol.44
    • Kac, V.G.1
  • 26
    • 0039580895 scopus 로고
    • Cambridge University Press, Cambridge
    • Kac, V. G., "Infinite Dimensional Lie Algebras," Progress in Math., Vol. 44 (Brikhäuser, Boston, 1983); 2nd ed. (Cambridge University Press, Cambridge, 1985); 3rd ed. (Cambridge University Press, Cambridge 1990).
    • (1985) Progress in Math., 2nd Ed.
  • 27
    • 0040172236 scopus 로고
    • Cambridge University Press, Cambridge
    • Kac, V. G., "Infinite Dimensional Lie Algebras," Progress in Math., Vol. 44 (Brikhäuser, Boston, 1983); 2nd ed. (Cambridge University Press, Cambridge, 1985); 3rd ed. (Cambridge University Press, Cambridge 1990).
    • (1990) Progress in Math., 3rd Ed.
  • 29
    • 0001098130 scopus 로고
    • Lectures on the infinite wedge representation and the MKP hierarchy
    • Presses Univ. Montreal, Montreal
    • Kac, V. G. and Peterson, D. H., "Lectures on the infinite wedge representation and the MKP hierarchy," Sem. Math. Sup., Vol. 102 (Presses Univ. Montreal, Montreal, 1986), pp. 141-184.
    • (1986) Sem. Math. Sup. , vol.102 , pp. 141-184
    • Kac, V.G.1    Peterson, D.H.2
  • 30
    • 18844422980 scopus 로고
    • Quasifinite highest weight modules over the Lie algebra of differential operators on the circle
    • Kac, V. and Radul, A., "Quasifinite highest weight modules over the Lie algebra of differential operators on the circle," Commun. Math. Phys. 157, 429-457 (1993).
    • (1993) Commun. Math. Phys. , vol.157 , pp. 429-457
    • Kac, V.1    Radul, A.2
  • 32
    • 0003290251 scopus 로고
    • Bombay lectures on highest weight representations of infinite-dimensional Lie algebras
    • World Scientific, Singapore
    • Kac, V. G. and Raina, A. K., Bombay lectures on highest weight representations of infinite-dimensional Lie algebras, Advanced Ser. in Math. Phys., Vol. 2 (World Scientific, Singapore, 1987).
    • (1987) Advanced Ser. in Math. Phys. , vol.2
    • Kac, V.G.1    Raina, A.K.2
  • 34
    • 0003193362 scopus 로고    scopus 로고
    • The geometry of spinors and the multicomponent BKP and DKP hierarchies, The bispectral problem
    • Montreal, 1997 (AMS, Providence, RI)
    • Kac, V. G. and van de Leur, J. W., "The geometry of spinors and the multicomponent BKP and DKP hierarchies, The bispectral problem," Montreal, 1997, CRM Proc. Lecture Notes, Vol. 14 (AMS, Providence, RI, 1998), pp. 159-202.
    • (1998) CRM Proc. Lecture Notes , vol.14 , pp. 159-202
    • Kac, V.G.1    Van de Leur, J.W.2
  • 35
    • 0001082536 scopus 로고
    • Exceptional hierarchies of soliton equations
    • Kac, V. G. and Wakimoto, M., "Exceptional hierarchies of soliton equations," Proc. Symp. Pure Math. 49, 191-237 (1989).
    • (1989) Proc. Symp. Pure Math. , vol.49 , pp. 191-237
    • Kac, V.G.1    Wakimoto, M.2
  • 36
    • 0002197536 scopus 로고
    • Realization of the basic representations of the Euclidean Lie algebras
    • Kac, V. G., Kazhdan, D. A., Lepowsky, J., and Wilson, R. L., "Realization of the basic representations of the Euclidean Lie algebras," Adv. Math. 42, 83-112 (1981).
    • (1981) Adv. Math. , vol.42 , pp. 83-112
    • Kac, V.G.1    Kazhdan, D.A.2    Lepowsky, J.3    Wilson, R.L.4
  • 38
    • 0007012325 scopus 로고
    • Complete integrability of the Kadomtsev-Petviashvili equation
    • Mulase, M., "Complete integrability of the Kadomtsev-Petviashvili equation," Adv. Math. 54, 57-66 (1984).
    • (1984) Adv. Math. , vol.54 , pp. 57-66
    • Mulase, M.1
  • 39
    • 0002833148 scopus 로고
    • Solvability of the super KP equation and a generalization of the Birkhoff decomposition
    • Mulase, M., "Solvability of the Super KP equation and a generalization of the Birkhoff decomposition," Invent. Math. 92, 1-46 (1988).
    • (1988) Invent. Math. , vol.92 , pp. 1-46
    • Mulase, M.1
  • 41
    • 0009145135 scopus 로고
    • Additional symmetries for integrable and conformal algebra representations
    • Orlov, A. Y. and Schulman, E. I., "Additional symmetries for integrable and conformal algebra representations," Lett. Math. Phys. 12, 171 (1986).
    • (1986) Lett. Math. Phys. , vol.12 , pp. 171
    • Orlov, A.Y.1    Schulman, E.I.2
  • 42
    • 0000148293 scopus 로고
    • Infinite flag varieties and conjugacy theorems
    • Peterson, D. H. and Kac, V. G., "Infinite flag varieties and conjugacy theorems," Proc. Natl. Acad. Sci. U.S.A. 80, 1778-1782 (1983).
    • (1983) Proc. Natl. Acad. Sci. U.S.A. , vol.80 , pp. 1778-1782
    • Peterson, D.H.1    Kac, V.G.2
  • 43
    • 0001841091 scopus 로고
    • Soliton equations as dynamical systems on infinite dimensional Grassmann manifolds
    • Sato, M., "Soliton equations as dynamical systems on infinite dimensional Grassmann manifolds," Res. Inst. Math. Sci. Kokyuroku 439, 30-46 (1981).
    • (1981) Res. Inst. Math. Sci. Kokyuroku , vol.439 , pp. 30-46
    • Sato, M.1
  • 45
    • 0001739042 scopus 로고
    • Characterization of Jacobian varieties in terms of soliton equations
    • Shiota, T., "Characterization of Jacobian varieties in terms of soliton equations," Invent. Math. 83, 333-382 (1986).
    • (1986) Invent. Math. , vol.83 , pp. 333-382
    • Shiota, T.1
  • 46
    • 0001565658 scopus 로고
    • Kinks and the Dirac equation
    • Skyrme, T. H. R., "Kinks and the Dirac equation," J. Math. Phys. 12, 735-1743 (1971).
    • (1971) J. Math. Phys. , vol.12 , pp. 735-1743
    • Skyrme, T.H.R.1
  • 49
    • 0002596374 scopus 로고
    • Toda lattice hierarchy
    • North-Holland, Amsterdam
    • Ueno, K. and Takasaki, K., "Toda lattice hierarchy," Adv. Stud. Pure Math., Vol. 4 (North-Holland, Amsterdam, 1984), pp. 1-95.
    • (1984) Adv. Stud. Pure Math. , vol.4 , pp. 1-95
    • Ueno, K.1    Takasaki, K.2
  • 50
    • 0030526116 scopus 로고    scopus 로고
    • s)-symmetries of the s-component KP hierarchy
    • s)-symmetries of the s-component KP hierarchy," J. Math. Phys. 37, 2315-2337 (1996).
    • (1996) J. Math. Phys. , vol.37 , pp. 2315-2337
    • Van de Leur, J.W.1
  • 51
    • 0032372275 scopus 로고    scopus 로고
    • Schlesinger-Bäcklund transformations for the N-component KP
    • van de Leur, J. W., "Schlesinger-Bäcklund transformations for the N-component KP," J. Math. Phys. 39, 2833-2847 (1998).
    • (1998) J. Math. Phys. , vol.39 , pp. 2833-2847
    • Van de Leur, J.W.1
  • 53
    • 0035627643 scopus 로고    scopus 로고
    • Matrix integrals and the geometry of spinors
    • van de Leur, J. W., "Matrix integrals and the geometry of spinors," J. Nonlinear Math. Phys. 8, 288-310 (2001).
    • (2001) J. Nonlinear Math. Phys. , vol.8 , pp. 288-310
    • Van de Leur, J.W.1
  • 54
    • 0002283027 scopus 로고
    • On two construction of conservation laws for Lax equations
    • Wilson, G., "On two construction of conservation laws for Lax equations," Q. J. Math. 32, 491-512 (1981).
    • (1981) Q. J. Math. , vol.32 , pp. 491-512
    • Wilson, G.1
  • 55
    • 0001841378 scopus 로고
    • The τ-function of the gAKNS equations
    • Integrable Systems (Luminy, 1991) Birkhuser, Boston
    • Wilson, G., "The τ-function of the gAKNS equations," Integrable Systems (Luminy, 1991), pp. 131-145, Progr. Math., Vol. 115 (Birkhuser, Boston, 1993).
    • (1993) Progr. Math. , vol.115 , pp. 131-145
    • Wilson, G.1


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