Scalar products of symmetric functions and matrix integrals

Theoretical and Mathematical Physics

Volumn 137, Issue 3, 2003, Pages 1676-1690

  Harnad, J ^a,b   Orlov, A Yu ^c  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b Gina Cody School of Engineering and Computer Science   (Canada)

^c SHIRSHOV INSTITUTE OF OCEANOLOGY   (Russian Federation)

Author keywords

Hypergeometric functions; Matrix models; Statistical sums; Symmetric functions; Tau functions; Toda lattices

Indexed keywords

EID: 3943071072     PISSN: 00405779     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:TAMP.0000007916.13779.17     Document Type: Conference Paper

References (21)

1. I. G. Macdonald, Symmetric Functions and Hall Polynomials, Clarendon, Oxford (1995).
2. M. Feigin and A. P. Veselov, Internat. Math. Res. Notices, 10, 521-545 (2002).
3. A. Yu. Orlov and D. M. Shcherbin, Theor. Math. Phys., 128, 906-926 (2001).
4. E. Date, M. Jimbo, M. Kashiwara, and T. Miwa, "Transformation groups for soliton equations," in: Nonlinear Integrable Systems: Classical Theory and Quantum Theory (Proc. RIMS Symp., Kyoto, M. Jimbo and T. Miwa, eds.), World Scientific, Singapore (1981), pp. 39-120.
5. K. Ueno and K. Takasaki, Adv. Stud. Pure Math., 4, 1-95 (1984).
6. V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Theory of Solitons: The Inverse Scattering Method [in Russian], Nauka, Moscow (1980); English transl.: S. P. Novikov, S. V. Manakov, L. P. Pitaevsky, and V. E. Zakharov, Plenum, New York (1984).
7. L. A. Dickey, Soliton Equations and Hamiltonian Systems (Adv. Ser. Math. Phys., Vol. 12), World Scientific, Singapore (1991).
8. P. Winternitz and A. Yu. Orlov, Theor. Math. Phys., 113, 1393-1417 (1997).
9. K. Takasaki, Comm. Math. Phys., 181, 131-156 (1996).
10. A. Yu. Orlov, "Soliton theory, symmetric functions, and matrix integrals," nlin.SI/0207030 (2002).
11. T. Takebe, Lett. Math. Phys., 21, 77-84 (1991).
12. L.-L. Chau and O. Zaboronsky, Comm. Math. Phys., 196, 203-247 (1998); hep-th/9711091 (1997).
13. M. Mineev-Weinstein, P. Wiegmann, and A. Zabrodin, Phys. Rev. Lett., 84, 5106-5109 (2000).
14. J. Harnad and A. Yu. Orlov, "Matrix integrals as Borel sums of Schur function expansions," in: Symmetry and Perturbation Theory (Proc. Intl. Conf. SPT 2002, Gala Gonone, Sardinia, Italy, 16-26 May 2002, S. Abenda, G. Gaeta, and S. Walcher, eds.), World Scientific, Singapore (2003); Preprint CRM-2865, CRM, Montreal (2002); nlin.SI/0209035 (2002).
15. J. Harnad and A. Yu. Orlov, "Schur function expansions of matrix integrals," Preprint CRM, CRM, Montreal (2002).
16. M. L. Mehta, Random Matrices (2nd ed.), Acad. Press, San Diego (1991).
17. C. Itzykson and J. B. Zuber, J. Math. Phys., 21, 411-421 (1980).
18. A. Gerasimov, A. Marshakov, A. Mironov, A. Morozov, and A. Orlov, Nucl. Phys. B, 357, 565-618 (1991).
19. M. Bertola, B. Eynard, and J. Harnad, J. Phys. A, 36, 3067-3084 (2003); nlin.SI/0204054 (2002).
20. B. Eynard, "Random matrices," Cours de Physique Theorique de Saclay, Preprint Saclay-T01/014, CRM-2708, Saclay, Paris (2001).
21. Yu. Klimov, A. Korzh, and S. Natanzon, "From 2D Toda hierarchy to conformal map for domains of Riemann sphere," math.NA/0212361 (2002).