Baxter operator and Archimedean Hecke algebra

Communications in Mathematical Physics

Volumn 284, Issue 3, 2008, Pages 867-896

  Gerasimov, A ^a,b   Lebedev, D ^a,c   Oblezin, S ^a,c  

^a INSTITUTE FOR THEORETICAL AND EXPERIMENTAL PHYSICS   (Russian Federation)

^b TRINITY COLLEGE DUBLIN   (Ireland)

^c MAX PLANCK INSTITUT FÜR MATHEMATIK   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 55149083730     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-008-0547-9     Document Type: Article

References (38)

1. Baxter R.J.: Exactly solved models in statistical mechanics. Academic Press, London (1982)
2. A. Berenstein A. Zelevinsky 1989 Tensor product multiplicities and convex polytopes in partition space J. Geom. Phys. 5 453 472
3. Bump, D.: The Rankin-Selberg method: A survey. In: Number Theory, Trace Formulas and Discrete Groups: Symposium in Honor of Atle Selberg (Oslo, Norway, July 14-21, 1987), London: Academic Press, (1989)
4. W. Casselman J. Shalika 1980 The unramified principal series of p-adic groups II The Whittaker function. Comp. Math. 41 207 231
5. Etingof, P.: Whittaker functions on quantum groups and q-deformed Toda operators. Amer. Math. Soc. Transl. Ser.2, 194, Providence, RI: Amer. Math. Soc., 1999, pp. 9-25
6. A. Gerasimov S. Kharchev D. Lebedev 2004 Representation Theory and Quantum Inverse Scattering Method: Open Toda Chain and Hyperbolic Sutherland Model Int. Math. Res. Notices 17 823 854
7. Gerasimov, A., Kharchev, S., Lebedev, D., Oblezin, S.: On a Gauss-Givental representation for quantum Toda chain wave function. Int. Math. Res. Notices, Volume 2006, Article ID 96489, 23 p.
8. Gerasimov, A., Lebedev, D., Oblezin, S.: Givental representation for classical groups. http://arxiv.org/list/math.RT/0608152, 2006
9. n. http://arxiv.org/list/math.RT/0609082, 2006
10. Gerasimov, A., Lebedev, D., Oblezin, S.: New Integral Representations of Whittaker Functions for Classical Lie Groups. http://arxiv.org/abs/0705.2886, 2007
11. Givental, A.: Stationary Phase Integrals, Quantum Toda Lattices, Flag Manifolds and the Mirror Conjecture. In: Topics in Singularity Theory, Amer. Math. Soc. Transl. Ser., 2 180, Providence, RI: Amer. Math. Soc., 1997, pp. 103-115
12. Goldfeld D.: Automorphic forms and L-functions for the group GL(N, R). Cambridge studies in Adv. Math. Cambridge Univ. Press, Cambridge (2006)
13. R.A. Gustafson 1994 Some q-beta and Mellin-Barnes integrals on compact Lie groups and Lie algebras Trans. Amer. Math. Soc. 341 1 69 119
14. Harish-Chandra 1958 Spherical functions on a semisimple Lie group I, II Amer. J. Math. 80 241 310 553-613
15. M. Hashizume 1982 Whittaker functions on semi-simple Lie groups Hiroshima Math. J. 12 259 293
16. H. Jacquet 1967 Fonctions de Whittaker associées aux groupes de Chevalley Bull. Soc. Math. France 95 243 309
17. H. Jacquet I.I. Piatetski-Shapiro J. Shalika 1983 Rankin-Selberg convolutions Amer. J. Math. 105 367 464
18. Jacquet H., Shalika J.: Rankin-Selberg convolution: the Archimedean theory. In: (eds) Festshrift in Honor of Piatetski-Shapiro, Part I, pp. 125-207. Amer. Math. Soc., Providence, RI (1990)
19. D. Joe B. Kim 2003 Equivariant mirrors and the Virasoro conjecture for flag manifolds Int. Math. Res. Notices 15 859 882
20. Kac V.: Infinite-dimensional Lie algebras. Cambridge University Press, Cambridge (1990)
21. S. Kharchev D. Lebedev 2000 Eigenfunctions of GL(N, R) Toda chain: The Mellin-Barnes representation JETP Lett. 71 235 238
22. S. Kharchev D. Lebedev 2001 Integral representations for the eigenfunctions of quantum open and periodic Toda chains from QISM formalism J. Phys. A 34 2247 2258
23. Kostant, B.: Quantization and representation theory. In: Representation theory of Lie groups. 34, London Math. Soc. Lecture Notes Series, London. Math. Soc., 1979, pp. 287-316
24. B. Kostant 1978 On Whittaker vectors and representation theory Invent. Math. 48 2 101 184
25. A.N. Parshin 1976 On the arithmetic of 2-dimensional schemes. I, Repartitions and residues Russ. Math. Izv. 40 736 773
26. V. Pasquier M. Gaudin 1992 The periodic Toda chain and a matrix generalization of the Bessel function recursion relation J. Phys. A 25 5243 5252
27. Reyman, A.G., Semenov-Tian-Shansky, M.A.: Integrable Systems. Group theory approach. Modern Mathematics, Moscow-Igevsk: Institute Computer Sciences, 2003
28. Serre, J.-P.: Facteurs locaux des fonctions zêta des variétés algébraiques (définisions et conjecures). Sém. Delange-Pisot-Poitou, exp. 19, 1969/70
29. n Ann. Math. 100 1 171 193
30. n over padic fields Proc. Japan Acad. 52 180 182
31. E. Stade 1990 On explicit integral formulas for GL(n, ℝ)-Whittaker functions Duke Math. J. 60 2 313 362
32. E. Stade 2001 Mellin transforms of GL(n, ℝ) Whittaker functions Amer. J. Math. 123 121 161
33. E. Stade 2002 Archimedean L-functions and Barnes integrals Israel J. Math. 127 201 219
34. T. Ishii E. Stade 2007 New formulas for Whittaker functions on GL(N, R) J. Funct. Anal. 244 289 314
35. Semenov-Tian-Shansky, M.: Quantum Toda lattices. Spectral theory and scattering. Preprint LOMI 3-84, 1984:
36. Quantization of open Toda lattices. In "Encyclodpaedia of Mathematical Sciences" 16. Dynamical systems VII. Berlin: Springer, 1994, pp. 226-259
37. I. Vinogradov L. Takhtadzhyan 1982 Theory of Eisenstein Series for the group SL(3, ℝ) and its application to a binary problem J. Soviet. Math. 18 293 324
38. Weil A.: Basic Number theory. Springer, Berlin (1967)