Norm of a Bethe vector and the Hessian of the master function

Compositio Mathematica

Volumn 141, Issue 4, 2005, Pages 1012-1028

  Mukhin, Evgeny ^a   Varchenko, Alexander ^b  

^a INDIANA UNIVERSITY   (United States)

^b University of North Carolina at Chapel Hill   (United States)

Author keywords

Bethe ansatz; Critical points; Master functions

Indexed keywords

EID: 43449115376     PISSN: 0010437X     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0010437X05001569     Document Type: Article

References (24)

1. H. Babujian, Off-shell Bethe ansatz equations and N-point correlators in the SU(2) WZNW theory, J. Phys. A 26 (1993), 6981-6990.
2. H. Babujian and R. Flume. Off-shell Bethe ansatz equation for Gaudin magnets and solutions of Knizhnik-Zamolodchikov equations, Modern Phys. Lett. A 9 (1994). 2029-2039.
3. N. M. Bogoliubov, A. G. Izergin and V. E. Korepin, Quantum inverse scattering method, and, correlation functions (Cambridge University Press. Cambridge, 1993).
4. D. Eisenbud and J. Harris, Divisors on general curves and cuspidal rational curves, Invent. Math. 74 (1983), 371-418.
5. L. D. Faddeev, Lectures on quantum inverse scattering method, in Integrable systems, Nankai Lectures Math. Phys., ed. X.-C. Song (World Scientific, Singapore, 1990), 23-70.
6. B. Feigin, E. Frenkel and N. Reshetikhin, Gaudin model, Bethe ansatz and critical level, Comrn. Math. Phys. 166 (1994), 27-62.
7. G. Felder, Y. Markov, V. Tarasov and A. Varchenko, Differential equations compatible with KZ equations, Math. Phys. Anal. Geom. 3 (2000), 139-177.
8. E. Frenkel, Affine algebras, Langlands duality and Bethe ansatz, in XIth International Congress of Mathematical Physics (Paris, 1994) (Internal. Press, Cambridge, MA, 1995), 606-642.
9. E. Frenkel, Opers on the projective line, flag manifolds and Bethe ansatz, Mosc. Math. J. 4 (2004), 655-705, 783.
10. B. Feigin, V. Schechtman and A. Varchenko, On algebraic equations satisfied by hyperqeometric correlators in WZW models, II, Comrn. Math. Phys. 170 (1995), 219-247.
11. L. D. Faddeev and L. A. Takhtajan, Quantum inverse problem method and the Heisenberg XYZ-model Russian Math. Surveys 34 (1979), 11-68.
12. M. Gaudin, Diagonalisation d'une classe d'Hamütoniens de spin, J. Physique 37 (1976), 1089-1098.
13. V. Kae, Infinite-dimensional Lie algebras (Cambridge University Press, Cambridge, 1990).
14. V. Korepin, Calculation of norms of Bethe wave functions, Comm. Math. Phys. 86 (1982), 391-418.
15. E. Mukhin and A. Varchenko, Remarks on critical points of phase functions and norms of Bethe vectors, Adv. Stud. Pure Math. 27 (2000), 239-246.
16. E. Mukhin and A. Varchenko, Miura opers and critical points of master functions, Preprint (2003), Math.QA/0312406.
17. E. Mukhin and A. Varchenko, Critical points of master functions and flag varieties, Commun. Contemp. Math. 6 (2004), 111-163.
18. N. Reshetikhin, Calculation of the norm, of Bethe vectors in models with SU(3) symmetry, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 150 (1986), 196-213.
19. N. Reshetikhin and A. Varchenko, Quasiclassical asymptocs of solutions to the KZ equations, in Geometry, topology and physics for R. Bott (Internat. Press, Cambridge, MA, 1995), 293-322.
20. F. Sottile, The special Schubert calculus is real, Electron. Res. Announc. Amer. Math. Soc. 5 (1999), 35-39.
21. V. Schechtman and A. Varchenko, Arrangements of hyperplanes and Lie algebra homology, Invent. Math. 106 (1991), 139-194.
22. 2 representations, and Fuchsian differential equations with only univalued solutions, Mosc. Math. J. 3 (2003), 621-645.
23. V. Tarasov and A. Varchenko, Asymptotic solutions to the quantized, Knizhnik-Zamolodchikov equation and Bethe vectors, Amer. Math. Soc. Transl. Ser. 2 174 (1996), 235-273.
24. A. Varchenko, Critical points of the product of powers of linear functions and families of bases of singular vectors, Compositio Math. 97 (1995), 385-401.