Minimal representations, spherical vectors and exceptional theta series

Communications in Mathematical Physics

Volumn 226, Issue 1, 2002, Pages 1-40

  Kazhdan, David ^a   Pioline, Boris ^b,d   Waldron, Andrew ^c,e  

^a HARVARD UNIVERSITY   (United States)

^b LPTHE   (France)

^c BRANDEIS UNIVERSITY   (United States)

^d HARVARD UNIVERSITY   (United States)

^e UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036002923     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200200601     Document Type: Article

References (37)

1. 4 couplings, the fundamental membrane and exceptional theta correspondences. JHEP 0103, 036 (2001), hep-th/0102123
2. Green, M.B., and Gutperle, M.: Effects of D instantons. Nucl. Phys. B498, 195-227 (1997), hep-th/9701093
3. 4 threshold corrections in IIB string theory and (p, q) string instantons. Nucl. Phys. B508, 509-534 (1997), hep-th/9707018; Pioline, B., and Kiritsis, E.: U-duality and D-brane combinatorics. Phys. Lett. B418, 61 (1998), hep-th/9710078
4. 4 threshold corrections in IIB string theory and (p, q) string instantons. Nucl. Phys. B508, 509-534 (1997), hep-th/9707018; Pioline, B., and Kiritsis, E.: U-duality and D-brane combinatorics. Phys. Lett. B418, 61 (1998), hep-th/9710078
5. 4 couplings. Phys. Lett. B 431, 73 (1998) hep-th/9804023; Green, M.B., and Sethi, S.: Supersymmetry constraints on type IIB supergravity: Phys. Rev. D 59, 046006 (1999) hep-th/9808061
6. 4 couplings. Phys. Lett. B 431, 73 (1998) hep-th/9804023; Green, M.B., and Sethi, S.: Supersymmetry constraints on type IIB supergravity: Phys. Rev. D 59, 046006 (1999) hep-th/9808061
7. Obers, N.A., and Pioline, B.: Eisenstein series and string thresholds. Commun. Math. Phys. 209, 275 (2000), hep-th/9903113; Obers, N.A., and Pioline, B.: Eisenstein series in string theory. Class. Quant. Grav. 17, 1215 (2000), hep-th/9910115
8. Obers, N.A., and Pioline, B.: Eisenstein series and string thresholds. Commun. Math. Phys. 209, 275 (2000), hep-th/9903113; Obers, N.A., and Pioline, B.: Eisenstein series in string theory. Class. Quant. Grav. 17, 1215 (2000), hep-th/9910115
9. Obers, N.A., and Pioline, B.: U-duality and M-theory. Phys. Rept. 318, 113 (1999), hep-th/9809039; Obers, N.A., and Pioline, B.: U-duality and M-theory, an algebraic approach, hep-th/9812139
10. Obers, N.A., and Pioline, B.: U-duality and M-theory. Phys. Rept. 318, 113 (1999), hep-th/9809039; Obers, N.A., and Pioline, B.: U-duality and M-theory, an algebraic approach, hep-th/9812139
11. Green, M.B., Gutperle, M., and Vanhove, P.: One loop in eleven dimensions. Phys. Lett. B 409, 177 (1997) hep-th/9706175; Green, M.B., Kwon, H.h., and Vanhove, P.: Phys. Rev. D 61, 104010 (2000) hep-th/9910055; Chalmers, G.: M-theory and automorphic scattering, hep-th/0104132
12. Green, M.B., Gutperle, M., and Vanhove, P.: One loop in eleven dimensions. Phys. Lett. B 409, 177 (1997) hep-th/9706175; Green, M.B., Kwon, H.h., and Vanhove, P.: Phys. Rev. D 61, 104010 (2000) hep-th/9910055; Chalmers, G.: M-theory and automorphic scattering, hep-th/0104132
13. Green, M.B., Gutperle, M., and Vanhove, P.: One loop in eleven dimensions. Phys. Lett. B 409, 177 (1997) hep-th/9706175; Green, M.B., Kwon, H.h., and Vanhove, P.: Phys. Rev. D 61, 104010 (2000) hep-th/9910055; Chalmers, G.: M-theory and automorphic scattering, hep-th/0104132
14. Sugino, F., and Vanhove, P.: U-duality from matrix membrane partition function, hep-th/0107145
15. Joseph, A.: Minimal realizations and spectrum generating algebras. Commun. Math. Phys. 36, 325 (1974); The minimal orbit in a simple Lie algebra and its associated maximal ideal. Ann. Scient. Ecole Normale Sup. 4ème série 9, 1-30 (1976)
16. Joseph, A.: Minimal realizations and spectrum generating algebras. Commun. Math. Phys. 36, 325 (1974); The minimal orbit in a simple Lie algebra and its associated maximal ideal. Ann. Scient. Ecole Normale Sup. 4ème série 9, 1-30 (1976)
17. 8. In: Functional Analysis on the Eve of the 21st century, Progress in Math. Basel-Boston: Birkhäuser, 1995
18. 8. In: Functional Analysis on the Eve of the 21st century, Progress in Math. Basel-Boston: Birkhäuser, 1995
19. 8. In: Functional Analysis on the Eve of the 21st century, Progress in Math. Basel-Boston: Birkhäuser, 1995
20. Kazhdan, D., and Savin, G.: The smallest representation of simply laced groups. Israel Math. Conf. Proceedings, Piatetski-Shapiro Festschrift 2, 209-223 (1990)
21. Howe, R.: θ-series and invariant theory. Proceedings of Symposia in Pure Mathematics XXXIII. Providence, RI: AMS, 1979
22. Kazhdan, D., and Polishchuk, A.: Spherical vector in the minimal representation of a simply-laced p-adic group. To appear
23. Lion, G., and Vergne, M.: The Weil representation, Maslov index and theta series. Progress in Mathematics 6, Basel-Boston: Birkhäuser, 1980; Mumford, D.: Tata lectures on Theta III. Progress in Mathematics, Basel-Boston: Birkhäuser, 1991
24. Lion, G., and Vergne, M.: The Weil representation, Maslov index and theta series. Progress in Mathematics 6, Basel-Boston: Birkhäuser, 1980; Mumford, D.: Tata lectures on Theta III. Progress in Mathematics, Basel-Boston: Birkhäuser, 1991
25. Terras, A.: Harmonic Analysis on Symmetric Spaces and Applications II. New-York: Springer-Verlag, 1985
26. Brekke, L., and Freund, P.G.O.: p-adic numbers in physics. Phys. Rep. 233, 1 (1993)
27. Gelfand, I., Graev, M., and Pjatetskii-Shapiro, I.: Representation theory and automorphic functions. London: Saunders, 1969
28. Gunaydin, M., Koepsell, K., and Nicolai, H.: Conformal and quasiconformal realizations of exceptional Lie groups. Commun. Math. Phys. 221, 57 (2001) hep-th/0008063
29. 4. In: Operator algebras, Unitary representations, enveloping algebras and invariant theories, A. Connes, M. Duflo, A. Joseph, R. Rentschler, eds., Progress in Mathematics 92, Boston: Birkhäuser, 1990, p. 125
30. Etingof, P., Kazhdan, D., and Polishchuk, A.: When is the Fourier transform of an elementary function elementary? math.AG/0003009
31. Kiritsis, E., Obers, N.A., and Pioline, B.: Heterotic/type II triality and instantons on K3. JHEP 0001, 029 (2000), hep-th/0001083
32. Nahm, W., and Wendland, K.: A hiker's guide to K3: Aspects of N = (4, 4) superconformal field theory with central charge c = 6. Commun. Math. Phys. 216, 85 (2001) hep-th/9912067.
33. 8(8). hep-th/0109005
34. 2. Invent. Math. 116, 677-791 (1994)
35. Vogan, D.: Singular unitary representations. Lecture Notes in Math. 880, Berlin-Heidelberg-New York: Springer Verlag
36. de Alfaro, V., Fubini, S., and Furlan, G.: Conformal Invariance In Quantum Mechanics. Nuovo Cim. A 34, 569 (1976)
37. Vermaseren, J.A.M.: New Features of Form. math-ph/0010025