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Published online by Cambridge University Press: 30 July 2009
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- Affine Hecke Algebras and Orthogonal Polynomials , pp. 170 - 172Publisher: Cambridge University PressPrint publication year: 2003
References
[A1] G. E. Andrews, Problems and prospects for basic hypergeometric functions. In Theory and Applications of Special Functions, ed. R. Askey, Academic Press, New York (1975)
[A2] and , Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Memoirs of the American Mathematical Society 319 (1985)Google Scholar
[B1] N. Bourbaki, Groupes et algèbres de Lie, Chapitres 4, 5 et 6, Hermann, Paris (1968)
[B3] and , Groupes réductifs sur un corps local: I. Données radicielles valuées, Publications Mathématiques de l'Institut des Hautes Études Scientifiques, no. 41 (1972)CrossRefGoogle Scholar
[C1] , Double affine Hecke algebras, Knizhnik — Zamolodchikov equations, and Macdonald's operators, International Mathematics Research Notices 9 (1992). 171–179CrossRefGoogle Scholar
[C2] , Double affine Hecke algebras and Macdonald's conjectures, Ann. Math.. 141 (1995) 191–216CrossRefGoogle Scholar
[C3] , Non-symmetric Macdonald polynomials, International Mathematics Research Notices 10 (1995) 483–515CrossRefGoogle Scholar
[C4] , Macdonald's evaluation conjectures and difference Fourier transform, Inv. Math.. 122 (1995) 119–145CrossRefGoogle Scholar
[C5] , Intertwining operators of double affine Hecke algebras, Sel. Math. new series 3 (1997) 459–495CrossRefGoogle Scholar
[D1] , Statistical theory of the energy levels of complex systems I, J. Math. Phys.. 3 (1962) 140–156CrossRefGoogle Scholar
[G1] G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press (1990)
[G2] , A generalization of Selberg's beta integral, Bulletin of the American Mathematical Society 22 (1990) 97–105CrossRefGoogle Scholar
[H1] and , Root systems and hypergeometric functions I, Comp. Math.. 64 (1987) 329–352Google Scholar
[I1] B. Ion, Involutions of double affine Hecke algebras, preprint (2001)
[K1] V. G. Kac, Infinite Dimensional Lie Algebras, Birkhäuser, Boston (1983)
[K2] , Lectures on affine Hecke algebras and Macdonald's conjectures, Bulletin of the American Mathematical Society 34 (1997) 251–292CrossRefGoogle Scholar
[K3] , Askey-Wilson polynomials for root systems of type BC, Contemp. Math. 138 (1992) 189–204CrossRefGoogle Scholar
[L1] , Affine Hecke algebras and their graded version, Journal of the American Mathematical Society 2 (1989) 599–635CrossRefGoogle Scholar
[M1] I. G. Macdonald, Spherical functions on a group of p-adic type, Publications of the Ramanujan Institute, Madras (1971)
[M2] , Affine root systems and Dedekind's η-function, Inv. Math. 15 (1972) 91–143CrossRefGoogle Scholar
[M3] , The Poincaré series of a Coxeter group, Math. Annalen 199 (1972) 161–174CrossRefGoogle Scholar
[M4] , Some conjectures for root systems, SIAM Journal of Mathematical Analysis 13 (1982) 988–1007CrossRefGoogle Scholar
[M5] , Orthogonal polynomials associated with root systems, preprint (1987); Séminaire Lotharingien de Combinatoire 45 (2000) 1–40Google Scholar
[M6] I. G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd edition, Oxford University Press (1995)
[M7] , Affine Hecke algebras and orthogonal polynomials, Astérisque 237 (1996) 189–207Google Scholar
[M8] , Symmetric functions and orthogonal polynomials, University Lecture Series vol. 12, American Mathematical Society (1998)Google Scholar
[M11] W. G. Morris, Constant Term Identities for Finite and Affine Root Systems: Conjectures and Theorems, Ph. D. thesis, Madison (1982)
[N1] , Macdonald — Koornwinder polynomials and affine Hecke rings, Sūriseisekikenkyūsho Kōkyūroku 919 (1995) 44–55 (in Japanese)Google Scholar
[O3] , Some applications of hypergeometric shift operators, Inv. Math. 98 (1989) 1–18CrossRefGoogle Scholar
[O4] , Harmonic analysis for certain representations of graded Hecke algebras, Acta Math. 175 (1995) 75–121CrossRefGoogle Scholar
[R1] , On the expansion of some infinite products, Proc. London Math. Soc. 24 (1893) 337–352Google Scholar
[R2] , Second memoir on the expansion of certain infinite products, Proc. London Math. Soc. 25 (1894) 318–343Google Scholar
[R3] , Third memoir on the expansion of certain infinite products, Proc. London Math. Soc. 26 (1895) 15–32Google Scholar
[S1] , Nonsymmetric Koornwinder polynomials and duality, Arm. Math. 150 (1999) 267–282Google Scholar
[S2] , Some properties of Koornwinder polynomials, Contemp. Math. 254 (2000) 395–411CrossRefGoogle Scholar
[S3] , Some combinatorial properties of Jack symmetric functions, Adv. in Math. 77 (1989) 76–115CrossRefGoogle Scholar
[S4] J. V. Stokman, Koornwinder polynomials and affine Hecke algebras, preprint (2000)
[V1] H. van der Lek, The Homotopy Type of Complex Hyperplane Arrangements, Thesis, Nijmegen (1983)
[V2] , Self-dual Koornwinder-Macdonald polynomials, Inv. Math. 126 (1996) 319–339CrossRefGoogle Scholar
[A1] G. E. Andrews, Problems and prospects for basic hypergeometric functions. In Theory and Applications of Special Functions, ed. R. Askey, Academic Press, New York (1975)
[A2] and , Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials, Memoirs of the American Mathematical Society 319 (1985)Google Scholar
[B1] N. Bourbaki, Groupes et algèbres de Lie, Chapitres 4, 5 et 6, Hermann, Paris (1968)
[B3] and , Groupes réductifs sur un corps local: I. Données radicielles valuées, Publications Mathématiques de l'Institut des Hautes Études Scientifiques, no. 41 (1972)CrossRefGoogle Scholar
[C1] , Double affine Hecke algebras, Knizhnik — Zamolodchikov equations, and Macdonald's operators, International Mathematics Research Notices 9 (1992). 171–179CrossRefGoogle Scholar
[C2] , Double affine Hecke algebras and Macdonald's conjectures, Ann. Math.. 141 (1995) 191–216CrossRefGoogle Scholar
[C3] , Non-symmetric Macdonald polynomials, International Mathematics Research Notices 10 (1995) 483–515CrossRefGoogle Scholar
[C4] , Macdonald's evaluation conjectures and difference Fourier transform, Inv. Math.. 122 (1995) 119–145CrossRefGoogle Scholar
[C5] , Intertwining operators of double affine Hecke algebras, Sel. Math. new series 3 (1997) 459–495CrossRefGoogle Scholar
[D1] , Statistical theory of the energy levels of complex systems I, J. Math. Phys.. 3 (1962) 140–156CrossRefGoogle Scholar
[G1] G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press (1990)
[G2] , A generalization of Selberg's beta integral, Bulletin of the American Mathematical Society 22 (1990) 97–105CrossRefGoogle Scholar
[H1] and , Root systems and hypergeometric functions I, Comp. Math.. 64 (1987) 329–352Google Scholar
[I1] B. Ion, Involutions of double affine Hecke algebras, preprint (2001)
[K1] V. G. Kac, Infinite Dimensional Lie Algebras, Birkhäuser, Boston (1983)
[K2] , Lectures on affine Hecke algebras and Macdonald's conjectures, Bulletin of the American Mathematical Society 34 (1997) 251–292CrossRefGoogle Scholar
[K3] , Askey-Wilson polynomials for root systems of type BC, Contemp. Math. 138 (1992) 189–204CrossRefGoogle Scholar
[L1] , Affine Hecke algebras and their graded version, Journal of the American Mathematical Society 2 (1989) 599–635CrossRefGoogle Scholar
[M1] I. G. Macdonald, Spherical functions on a group of p-adic type, Publications of the Ramanujan Institute, Madras (1971)
[M2] , Affine root systems and Dedekind's η-function, Inv. Math. 15 (1972) 91–143CrossRefGoogle Scholar
[M3] , The Poincaré series of a Coxeter group, Math. Annalen 199 (1972) 161–174CrossRefGoogle Scholar
[M4] , Some conjectures for root systems, SIAM Journal of Mathematical Analysis 13 (1982) 988–1007CrossRefGoogle Scholar
[M5] , Orthogonal polynomials associated with root systems, preprint (1987); Séminaire Lotharingien de Combinatoire 45 (2000) 1–40Google Scholar
[M6] I. G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd edition, Oxford University Press (1995)
[M7] , Affine Hecke algebras and orthogonal polynomials, Astérisque 237 (1996) 189–207Google Scholar
[M8] , Symmetric functions and orthogonal polynomials, University Lecture Series vol. 12, American Mathematical Society (1998)Google Scholar
[M11] W. G. Morris, Constant Term Identities for Finite and Affine Root Systems: Conjectures and Theorems, Ph. D. thesis, Madison (1982)
[N1] , Macdonald — Koornwinder polynomials and affine Hecke rings, Sūriseisekikenkyūsho Kōkyūroku 919 (1995) 44–55 (in Japanese)Google Scholar
[O3] , Some applications of hypergeometric shift operators, Inv. Math. 98 (1989) 1–18CrossRefGoogle Scholar
[O4] , Harmonic analysis for certain representations of graded Hecke algebras, Acta Math. 175 (1995) 75–121CrossRefGoogle Scholar
[R1] , On the expansion of some infinite products, Proc. London Math. Soc. 24 (1893) 337–352Google Scholar
[R2] , Second memoir on the expansion of certain infinite products, Proc. London Math. Soc. 25 (1894) 318–343Google Scholar
[R3] , Third memoir on the expansion of certain infinite products, Proc. London Math. Soc. 26 (1895) 15–32Google Scholar
[S1] , Nonsymmetric Koornwinder polynomials and duality, Arm. Math. 150 (1999) 267–282Google Scholar
[S2] , Some properties of Koornwinder polynomials, Contemp. Math. 254 (2000) 395–411CrossRefGoogle Scholar
[S3] , Some combinatorial properties of Jack symmetric functions, Adv. in Math. 77 (1989) 76–115CrossRefGoogle Scholar
[S4] J. V. Stokman, Koornwinder polynomials and affine Hecke algebras, preprint (2000)
[V1] H. van der Lek, The Homotopy Type of Complex Hyperplane Arrangements, Thesis, Nijmegen (1983)
[V2] , Self-dual Koornwinder-Macdonald polynomials, Inv. Math. 126 (1996) 319–339CrossRefGoogle Scholar