The Pfaff Lattice and Skew-orthogonal Polynomials

International Mathematics Research Notices

Volumn 1999, Issue 11, 1999, Pages

  Adler, M ^a   Horozov, E ^c   Van Moerbeke, P ^a,b  

^a BRANDEIS UNIVERSITY   (United States)

^b UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

^c NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347243206     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (12)

1. M. Adler, T. Shiota, and P. van Moerbeke, The Pfaffian τ-functions, to appear.
2. M. Adler and P. van Moerbeke, Completely integrable systems, Euclidean Lie algebras, and curves, Adv. Math. 38 (1980), 267-317.
3. _, Matrix integrals, Toda symmetries, Virasoro constraints, and orthogonal polynomials, Duke Math. J. 80 (1995), 863-911.
4. _, Group factorization, moment matrices, and 2-Toda lattices, IMRN (Internat. Math. Res. Notices) 1997, 555-572.
5. _, The Pfaff lattice, matrix integrals, and a map from Toda to Pfaff, to appear.
6. É. Brézin and H. Neuberger, Multicritical points of unoriented random surfaces, Nuclear Phys. B 350 (1991), 513-553.
7. L. Dickey, Soliton Equations and Integrable Systems, Adv. Ser. Math. Phys. 12, World Scientific, River Edge, NJ, 1991.
8. V. G. Kac, Infinite-Dimensional Lie Algebras, 3d ed., Cambridge University Press, Cambridge, 1990.
9. V. Kac and J. van de Leur, "The geometry of spinors and the multicomponent BKP and DKP hierarchies" in The Bispectral Problem (Montreal, PQ, 1997), CRM Proc. Lecture Notes 14, Amer. Math. Soc., Providence, 1998, 159-202.
10. M. L. Mehta, Random Matrices, 2d ed. Academic Press, Boston, 1991.
11. A. G. Reyman and M. A. Semenov-Tian-Shansky, Reduction of Hamiltonian systems, affine Lie algebras and Lax equations, Invent. Math. 54 (1979), 81-100.
12. P. van Moerbeke, "Integrable foundations of string theory" in Lectures on Integrable systems (Sophia-Antipolis, 1991), ed. O. Babelon, P. Cartier, and Y. Kosmann-Schwarzbach, Proceedings of the CIMPA-school, World Scientific, River Edge, NJ, 1994, 163-267.