메뉴 건너뛰기




Volumn 2000, Issue 6, 2000, Pages

Commutative Rings of Difference Operators and an Adelic Flag Manifold

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0346737803     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (55)

References (38)
  • 1
    • 0001837575 scopus 로고
    • Limit matrices for the Toda flow and periodic flags for loop groups
    • M. Adler, L. Haine, and P. van Moerbeke, Limit matrices for the Toda flow and periodic flags for loop groups, Math. Ann. 296 (1993), 1-33.
    • (1993) Math. Ann. , vol.296 , pp. 1-33
    • Adler, M.1    Haine, L.2    Van Moerbeke, P.3
  • 2
    • 34250282189 scopus 로고
    • On a class of polynomials connected with the Korteweg-de Vries equation
    • M. Adler and J. Moser, On a class of polynomials connected with the Korteweg-de Vries equation, Comm. Math. Phys. 61 (1978), 1-30.
    • (1978) Comm. Math. Phys. , vol.61 , pp. 1-30
    • Adler, M.1    Moser, J.2
  • 3
    • 0033244228 scopus 로고    scopus 로고
    • Vertex operator solutions to the Discrete KP-hierarchy
    • M. Adler and P. van Moerbeke, Vertex operator solutions to the Discrete KP-hierarchy, Comm. Math. Phys. 203 (1999), 185-210.
    • (1999) Comm. Math. Phys. , vol.203 , pp. 185-210
    • Adler, M.1    Van Moerbeke, P.2
  • 4
    • 0031549908 scopus 로고    scopus 로고
    • Bispectral algebras of commuting ordinary differential operators
    • B. Bakalov, E. Horozov, and M. Yakimov, Bispectral algebras of commuting ordinary differential operators, Comm. Math. Phys. 190 (1997), 331-373.
    • (1997) Comm. Math. Phys. , vol.190 , pp. 331-373
    • Bakalov, B.1    Horozov, E.2    Yakimov, M.3
  • 5
    • 0000032737 scopus 로고
    • Über Sturm-Liouvillesche Polynomsysteme
    • S. Bochner, Über Sturm-Liouvillesche Polynomsysteme, Math. Z. 29 (1929), 730-736.
    • (1929) Math. Z. , vol.29 , pp. 730-736
    • Bochner, S.1
  • 7
    • 0003252813 scopus 로고
    • Soliton Equations and Hamiltonian Systems
    • World Sci. Publishing, River Edge, NJ
    • L. A. Dickey, Soliton Equations and Hamiltonian Systems, Adv. Ser. Math. Phys. 12, World Sci. Publishing, River Edge, NJ, 1991.
    • (1991) Adv. Ser. Math. Phys. , vol.12
    • Dickey, L.A.1
  • 8
    • 0001353545 scopus 로고    scopus 로고
    • Modified KP and discrete KP
    • _, Modified KP and discrete KP, Lett. Math. Phys. 48 (1999), 277-289.
    • (1999) Lett. Math. Phys. , vol.48 , pp. 277-289
  • 9
    • 0001575148 scopus 로고
    • Differential equations in the spectral parameter
    • J. J. Duistermaat and F. A. Grünbaum, Differential equations in the spectral parameter, Comm. Math. Phys. 103 (1986), 177-240.
    • (1986) Comm. Math. Phys. , vol.103 , pp. 177-240
    • Duistermaat, J.J.1    Grünbaum, F.A.2
  • 11
    • 1842453908 scopus 로고    scopus 로고
    • Deformations of the KdV hierarchy and related soliton equations
    • E. Frenkel, Deformations of the KdV hierarchy and related soliton equations, Internat. Math. Res. Notices 1996, 55-76.
    • (1996) Internat. Math. Res. Notices , pp. 55-76
    • Frenkel, E.1
  • 12
    • 0003866733 scopus 로고    scopus 로고
    • Orthogonal polynomials satisfying differential equations: The role of the Darboux transformation
    • Symmetries and Integrability of Difference Equations (Estérel, PQ, 1994), Amer. Math. Soc., Providence
    • F. A. Grünbaum and L. Haine, "Orthogonal polynomials satisfying differential equations: the role of the Darboux transformation" in Symmetries and Integrability of Difference Equations (Estérel, PQ, 1994), 143-154, GRM Proc. Lecture Notes 9, Amer. Math. Soc., Providence, 1996.
    • (1996) GRM Proc. Lecture Notes , vol.9 , pp. 143-154
    • Grünbaum, F.A.1    Haine, L.2
  • 13
    • 0000517640 scopus 로고    scopus 로고
    • A theorem of Bochner, revisited
    • Algebraic Aspects of Integrable Systems, Birkhäuser, Boston
    • _, "A theorem of Bochner, revisited" in Algebraic Aspects of Integrable Systems, 143-172, Progr. Nonlinear Differential Equations 26, Birkhäuser, Boston, 1997.
    • (1997) Progr. Nonlinear Differential Equations , vol.26 , pp. 143-172
  • 14
    • 0000176933 scopus 로고    scopus 로고
    • Bispectral Darboux transformations: An extension of the Krall polynomials
    • _, Bispectral Darboux transformations: an extension of the Krall polynomials, Internat. Math. Res. Notices 1997, 359-392.
    • (1997) Internat. Math. Res. Notices , pp. 359-392
  • 15
    • 0032691309 scopus 로고    scopus 로고
    • Some functions that generalize the Krall-Laguerre polynomials
    • F. A. Grünbaum, L. Haine, and E. Horozov, Some functions that generalize the Krall-Laguerre polynomials, J. Comput. Appl. Math. 106 (1999), 271-297.
    • (1999) J. Comput. Appl. Math. , vol.106 , pp. 271-297
    • Grünbaum, F.A.1    Haine, L.2    Horozov, E.3
  • 16
    • 0002181885 scopus 로고    scopus 로고
    • Beyond the classical orthogonal polynomials
    • The Bispectral Problem (Montréal, PQ, 1997), Amer. Math. Soc., Providence
    • L. Haine, "Beyond the classical orthogonal polynomials" in The Bispectral Problem (Montréal, PQ, 1997), 47-65, CRM Proc. Lecture Notes 14, Amer. Math. Soc., Providence, 1998.
    • (1998) CRM Proc. Lecture Notes , vol.14 , pp. 47-65
    • Haine, L.1
  • 17
    • 0003282810 scopus 로고
    • Toda orbits of Laguerre polynomials and representations of the Virasoro algebra
    • L. Haine and E. Horozov, Toda orbits of Laguerre polynomials and representations of the Virasoro algebra, Bull. Sci. Math. (2) 117 (1993), 485-518.
    • (1993) Bull. Sci. Math. (2) , vol.117 , pp. 485-518
    • Haine, L.1    Horozov, E.2
  • 18
    • 0031582790 scopus 로고    scopus 로고
    • The bispectral property of a q-deformation of the Schur polynomials and the q-KdV hierarchy
    • L. Haine and P. Iliev, The bispectral property of a q-deformation of the Schur polynomials and the q-KdV hierarchy, J. Phys. A 30 (1997), 7217-7227.
    • (1997) J. Phys. A , vol.30 , pp. 7217-7227
    • Haine, L.1    Iliev, P.2
  • 19
    • 0000510464 scopus 로고    scopus 로고
    • Tau function solutions to a q-deformation of the KP hierarchy
    • P. Iliev, Tau function solutions to a q-deformation of the KP hierarchy, Lett. Math. Phys. 44 (1998), 187-200.
    • (1998) Lett. Math. Phys. , vol.44 , pp. 187-200
    • Iliev, P.1
  • 20
    • 0041125776 scopus 로고    scopus 로고
    • Solutions to Frenkel's deformation of the KP hierarchy
    • _, Solutions to Frenkel's deformation of the KP hierarchy, J. Phys. A 31 (1998), L241-L244.
    • (1998) J. Phys. A , vol.31
  • 21
    • 0001009854 scopus 로고    scopus 로고
    • Bispectral Darboux transformations: The generalized Airy case
    • A. Kasman and M. Rothstein, Bispectral Darboux transformations: The generalized Airy case, Phys. D 102 (1997), 159-176.
    • (1997) Phys. D , vol.102 , pp. 159-176
    • Kasman, A.1    Rothstein, M.2
  • 22
    • 0030697545 scopus 로고    scopus 로고
    • Extensions and contractions of the Lie algebra of q-pseudodifferential symbols on the circle
    • B. Khesin, V. Lyubashenko, and C. Roger, Extensions and contractions of the Lie algebra of q-pseudodifferential symbols on the circle, J. Funct. Anal. 143 (1997), 55-97.
    • (1997) J. Funct. Anal. , vol.143 , pp. 55-97
    • Khesin, B.1    Lyubashenko, V.2    Roger, C.3
  • 23
    • 0000181519 scopus 로고
    • Certain differential equations for the Tchebycheff polynomials
    • H. L. Krall, Certain differential equations for the Tchebycheff polynomials, Duke Math. J. 4 (1938), 705-718.
    • (1938) Duke Math. J. , vol.4 , pp. 705-718
    • Krall, H.L.1
  • 24
    • 0003272555 scopus 로고
    • On orthogonal polynomials satisfying a certain fourth order differential equation
    • _, On orthogonal polynomials satisfying a certain fourth order differential equation, Pennsylvania State College Studies 1940 (1940), 1-24.
    • (1940) Pennsylvania State College Studies , vol.1940 , pp. 1-24
  • 25
    • 0010989303 scopus 로고
    • Methods of algebraic geometry in the theory of non-linear equations
    • I. M. Krichever, Methods of algebraic geometry in the theory of non-linear equations, Russ. Math. Surveys 32 (1977), 185-214.
    • (1977) Russ. Math. Surveys , vol.32 , pp. 185-214
    • Krichever, I.M.1
  • 26
    • 0001776613 scopus 로고
    • Rational solutions of the Kadomtsev-Petviashvili equation and integrable systems of n particles on a line
    • _, Rational solutions of the Kadomtsev-Petviashvili equation and integrable systems of n particles on a line, Funct. Anal. Appl. 12 (1978), 59-61.
    • (1978) Funct. Anal. Appl. , vol.12 , pp. 59-61
  • 27
    • 0008807748 scopus 로고
    • Algebraic curves and nonlinear difference equations
    • _, Algebraic curves and nonlinear difference equations (in Russian), Uspekhi Mat. Nauk 33 (1978), 215-216.
    • (1978) Uspekhi Mat. Nauk , vol.33 , pp. 215-216
  • 28
    • 0001283637 scopus 로고
    • Differential-difference evolution equations II: Darboux transformation for the Toda lattice
    • V. B. Matveev and M. A. Salle, Differential-difference evolution equations II: Darboux transformation for the Toda lattice, Lett. Math. Phys. 3 (1979), 425-429.
    • (1979) Lett. Math. Phys. , vol.3 , pp. 425-429
    • Matveev, V.B.1    Salle, M.A.2
  • 29
    • 0000885783 scopus 로고
    • An algebro-geometric construction of commuting operators and of solutions to the Toda lattice equation, Korteweg-de Vries equation and related nonlinear equations
    • Kinokuniya Book Store, Tokyo
    • D. Mumford, "An algebro-geometric construction of commuting operators and of solutions to the Toda lattice equation, Korteweg-de Vries equation and related nonlinear equations" in Proceedings of International Symposium on Algebraic Geometry (Kyoto Univ., Kyoto, 1977), Kinokuniya Book Store, Tokyo, 1978, 115-153.
    • (1978) Proceedings of International Symposium on Algebraic Geometry (Kyoto Univ., Kyoto, 1977) , pp. 115-153
    • Mumford, D.1
  • 30
    • 0003358349 scopus 로고
    • Tata lectures on theta II. Jacobian theta functions and differential equations
    • Birkhäuser, Boston
    • _, Tata lectures on theta II. Jacobian theta functions and differential equations, Progr. Math. 43, Birkhäuser, Boston, 1984.
    • (1984) Progr. Math. , vol.43
  • 32
    • 0001739042 scopus 로고
    • Characterization of Jacobian varieties in terms of soliton equations
    • T. Shiota, Characterization of Jacobian varieties in terms of soliton equations, Invent. Math. 83 (1986), 333-382.
    • (1986) Invent. Math. , vol.83 , pp. 333-382
    • Shiota, T.1
  • 33
    • 36449007207 scopus 로고
    • Calogero-Moser hierarchy and KP-hierarchy
    • _, Calogero-Moser hierarchy and KP-hierarchy, J. Math. Phys. 35 (1994), 5844-5849.
    • (1994) J. Math. Phys. , vol.35 , pp. 5844-5849
  • 34
    • 0002596374 scopus 로고
    • Toda lattice hierarchy
    • Group Representations and Systems of Differential Equations (Tokyo, 1982), North-Holland, New York
    • K. Ueno and K. Takasaki, "Toda lattice hierarchy" in Group Representations and Systems of Differential Equations (Tokyo, 1982), Adv. Stud. Pure Math. 4, North-Holland, New York, 1984, 1-95.
    • (1984) Adv. Stud. Pure Math. , vol.4 , pp. 1-95
    • Ueno, K.1    Takasaki, K.2
  • 35
    • 0001827098 scopus 로고
    • The spectrum of difference operators and algebraic curves
    • P. van Moerbeke and D. Mumford, The spectrum of difference operators and algebraic curves, Acta Math. 143 (1979), 93-154.
    • (1979) Acta Math. , vol.143 , pp. 93-154
    • Van Moerbeke, P.1    Mumford, D.2
  • 36
    • 0041762875 scopus 로고
    • Bispectral commutative ordinary differential operators
    • G. Wilson, Bispectral commutative ordinary differential operators, J. Reine Angew. Math. 442 (1993), 177-204.
    • (1993) J. Reine Angew. Math. , vol.442 , pp. 177-204
    • Wilson, G.1
  • 37
    • 0009958584 scopus 로고    scopus 로고
    • Collisions of Calogero-Moser particles and an adelic Grassmannian
    • with an appendix by I. G. Macdonald
    • _, Collisions of Calogero-Moser particles and an adelic Grassmannian, with an appendix by I. G. Macdonald, Invent. Math. 133 (1998), 1-41.
    • (1998) Invent. Math. , vol.133 , pp. 1-41
  • 38
    • 0000263463 scopus 로고
    • Differential equations in the spectral parameter, Darboux transformations and a hierarchy of master symmetries for KdV
    • J. P. Zubelli and F. Magri, Differential equations in the spectral parameter, Darboux transformations and a hierarchy of master symmetries for KdV, Comm. Math. Phys. 141 (1991), 329-351.
    • (1991) Comm. Math. Phys. , vol.141 , pp. 329-351
    • Zubelli, J.P.1    Magri, F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.