Standard conjectures for the arithmetic Grassmannian G(2,N) and Racah polynomials

Duke Mathematical Journal

Volumn 110, Issue 2, 2001, Pages 359-376

  Kresch, Andrew ^a   Tamvakis, Harry ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33750185610     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-01-11027-2     Document Type: Article

References (24)

1. [AW] R. Askey and J. Wilson, A set of orthogonal polynomials that generalize the Racah coefficients or $6$-$j$ symbols, SIAM J. Math. Anal. 10 (1979), 1008-1016.
2. [BL] L. C. Biedenharn and J. D. Louck, The Racah-Wigner Algebra in Quantum Theory, Encyclopedia Math. Appl. 9, Addison-Wesley, Reading, Mass., 1981.
3. [BGS] J.-B. Bost, H. Gillet, and C. Soulé, Heights of projective varieties and positive Green forms, J. Amer. Math. Soc. 7 (1994), 903-1027.
4. [Fa] G. Faltings, Calculus on arithmetic surfaces, Ann. of Math. (2) 119 (1984), 387-424.
5. [Fu] W. Fulton, Intersection Theory, 2d ed., Ergeh. Math. Grenzgeb. (3) 2, Springer, Berlin, 1998.
6. [GS] H. Gillet and C. Soulé, "Arithmetic analogs of the standard conjectures" in Motives (Seattle, Wash., 1991), Proc. Sympos. Pure Math. 55, Part 1, Amer. Math. Soc., Providence, 1994, 129-140.
7. [Gr] A. Grothendieck, "Standard conjectures on algebraic cycles" in Algebraic Geometry (Bombay, 1968), Oxford Univ. Press, London, 1969, 193-199.
8. [Ho] H. Hochstadt, The Functions of Mathematical Physics, Pure Appl. Math. 23, Wiley-Interscience, New York, 1971.
9. [Hr] P. Hriljac, Heights and Arakelov's intersection theory, Amer. J. Math. 107 (1985), 23-38.
10. [Kl] S. L. Kleiman, "The standard conjectures" in Motives (Seattle, Wash., 1991), Proc. Sympos. Pure Math. 55, Part 1, Amer. Math. Soc., Providence, 1994, 3-20.
11. [Ku] K. Künnemann, Some remarks on the arithmetic Hodge index conjecture, Compositio Math. 99 (1995), 109-128.
12. [KM] K. Künnemann and V. Maillot, "Théorèmes de Lefschetz et de Hodge arithmétiques pour les variétés admettant une décomposition cellulaire" in Regulators in Analysis, Geometry and Number Theory, Progr. Math. 171, Birkhäuser, Boston, 2000, 197-205.
13. [KT] K. Künnemann and H. Tamvakis, The Hodge star operator on Schubert forms, to appear in Topology.
14. [NSU] A. F. Nikiforov, S. K. Suslov, and V. B. Uvarov, Classical Orthogonal Polynomials of a Discrete Variable (in Russian), "Nauka," Moscow, 1985, ; English translation in Springer Ser. Comput. Phys., Springer, Berlin, 1991.
15. [Ra] G. Racah, Theory of complex spectra, II, Physical Rev. 62 (1942), 438-462.
16. [Ro] R. Roy, Binomial identities and hypergeometric series, Amer. Math. Monthly 94 (1987), 36-46.
17. [So] C. Soulé, "Hermitian vector bundles on arithmetic varieties" in Algebraic Geometry (Santa Cruz, Calif., 1995), Proc. Sympos. Pure Math. 62, Part 1, Amer. Math. Soc., Providence, 1997, 383-419.
18. [St] R. P. Stanley, Enumerative Combinatorics, Vol. 2, Cambridge Stud. Adv. Math. 62, Cambridge Univ. Press, Cambridge, 1999.
19. [Sz] G. Szegö, Orthogonal Polynomials, 4th éd., Amer. Math. Soc. Colloq. Publ. 23, Amer. Math. Soc., Providence, 1975.
20. [Ta] Y. Takeda, A relation between standard conjectures and their arithmetic analogues, Kodai Math. J. 21 (1998), 249-258.
21. [T] H. Tamvakis, Schubert calculus on the arithmetic Grassmannian, Duke Math. J. 98 (1999), 421-443.
22. [VK] N. Ja. Vilenkin and A. U. Klimyk, Representation of Lie groups and Special Functions, Vol. 1: Simplest Lie Groups, Special Functions and Integral Transforms, trans. V. A. Groza and A. A. Groza, Math. Appl. (Soviet Ser.) 72, Kluwer, Dordrecht, 1991.
23. [Wh] F. J. W. Whipple, Well-poised series and other generalized hypergeometric series, Proc. London Math. Soc. (2) 25 (1926), 525-544.
24. [Wi] J. A. Wilson, Hypergeometric series, recurrence relations and some new orthogonal functions, Ph.D. thesis, University of Wisconsin, Madison, 1978.