Milne's hypergeometric functions in terms of free fermions

Journal of Physics A: Mathematical and General

Volumn 34, Issue 11, 2001, Pages 2295-2310

  Orlov, A Yu ^a,b   Scherbin, D M ^b  

^a KYOTO UNIVERSITY   (Japan)

^b SHIRSHOV INSTITUTE OF OCEANOLOGY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035937688     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/34/11/321     Document Type: Article

References (32)

1. Milne SC 1992 Summation theorems for basic hypergeometric series of Schur function argument Progress in Approximation Theory ed A A Gonchar and E B Saff (New York: Springer) pp 51-77
2. Takasaki K 1984 Initial value problem for the Toda lattice hierarchy Adv. Stud. Pure Math. 4 139-63
3. Takasaki K 1996 The Toda lattice hierarchy and generalized string equation Commun. Math. Phys. 181 131
4. (Takasaki K 1995 Preprint hep-th/9506089)
5. Takebe T and Takasaki K 1995 Rev. Math. Phys. 7 743-808
6. (Takebe T and Takasaki K 1994 Preprint hep-th/94050096)
7. Zakharov V E and Shabat A B 1974 J. Funct. Anal. Appl. 8,226
8. Zakharov V E and Shabat A B 1979 J. Funct. Anal. Appl. 13 166
9. Jimbo M and Miwa T 1983 Publ. RIMS Kyoto Univ. 19 943
10. Date E, Jimbo M, Kashiwara M and Miwa T 1983 Transformation groups for soliton equations Nonlinear Integrable Systems - Classical Theory and Quantum Theory ed M Jimbo and T Miwa (Singapore: World Scientific) pp 39-120
11. Dickey L A 1991 Soliton Equations and Hamiltonian System (Singapore: World Scientific)
12. Zakharov V E, Manakov S V, Novikov S P and Pitaevsky L P 1980 The Theory of Solitons. The Inverse Scattering Method (Moscow: Nauka)
13. Mikhailov A V 1979 On the integrability of two-dimensional generalization of the Toda lattice Lett. J. Exp. Theor. Phys. 30 443-8
14. Ueno K and Takasaki K 1984 Adv. Stud. Pure Math. 4 1-95
15. Vilenkin N Ya and Klimyk A U 1995 Representation of Lie groups and Special Functions (Dordrecht: Kluwer)
16. Vilenkin N Ya and Klimyk A U 1992 Representation of Lie Groups and Special Functions vol 3 Classical and Quantum Groups and Special Functions (Dordrecht: Kluwer)
17. Macdonald I G 1995 Symmetric Functions and Hall Polynomials (Oxford: Clarendon)
18. Orlov A Yu 1988 Vertex operators, ∂ bar problem, symmetries, Hamiltonian and Lagrangian formalism of (2 +1) dimensional integrable systems Proc. 3rd Kiev. Int. Workshop (1987) vol I (Singapore: World Scientific) pp 116-34
19. Morozov A Yu and Vinet L 1993 q-hypergeometric functions in the formalism of free fields Mod. Phys. Lett. A 8 2891-902
20. Kontsevich M 1991 Funk. Anal. ego Prilozh. 25 no 2 50-7
21. Gerasimov A, Marshakov A, Mironov A, Morozov A and Orlov A 1991 Nucl. Phys. B 565
22. Zabrodin A 1999 Commuting difference operators with elliptic coefficients from Baxter's vacuum vectors Preprinr QA/9912218
23. Frenkel I and Turaev V 1997 Elliptic solutions of the Yang-Baxter equations and modular hypergeometric functions The Arnold-Gelfand Mathematical Seminars (Boston, MA: Birkhäuser) pp 171-204
24. Zhedanov A and Spiridonov V 2000 Commun. Math. Phys. 210 49-83
25. Bogdanov L V 1995 Physica D 87 58-63
26. (Bogdanov L V 1995 Preprint q-alg/9501031)
27. Mironov A D 1998 Theor. Math. Phys. 114 127
28. (Mironov A D 1997 Preprint q-alg/9711006)
29. Tu Ming-Hsien 1999 Lett. Math. Phys. 49 95-103
30. Kravchenko O and Khesin B 1991 Funct. Anal. Appl. 25 83
31. Mehta M L 1991 Random Matrices (New York: Academic)
32. Okounkov A 2000 Toda equations for Hurwitz numbers Preprint math. AG/0004128