Ebook: ICM-90 Satellite Conference Proceedings: Special Functions

The 1990 Hayashibara Forum, "the International Conference on Special Functions", was held at Fujisaki Institute, Hayashibara Biochemical Laboratories, Inc., Okayama, Japan for five days (August 16-20, 1990). This volume is the proceedings for that meeting. On January 14,1985, Heisuke Hironaka and Ken Hayashibara, the president of Chair­ man, Board of Trustees, Hayashibara Foundation, met and decided to have an international conference on mathematics in the summer of 1990. This was pushed forward by Kiyosi Ito, who proposed "Special functions" as the theme of the conference. He also asked the present editors to join in the organizing committee of the Hayashibara Forum, 1990. On May 13, 1989 the organizing committee sent letters to major Japanese mathemat­ ical institutions asking their members to give suggestions about whom it should invite. Receiving the replies, the organizing committee decided the invited speakers, and sent invitation letters to them, in which it was written that "Special functions have been created and explored to describe scientific and mathematical phenomena. Trigonometric functions give the relation of angle to length. Riemann's zeta function was invented in order to describe the prime number distribution. Legendre's spherical functions and Bessel's functions were born in connection with the eigenvalue problems for partial differential equations.

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Contents: T. Aoki, T. Kawai, Y. Takei: The Bender-Wu Analysis and the Voros Theory.- K. Aomoto, Y. Kato: A q-Analogue of de Rham Cohomology.- I. Cherednik: Affine Extensions of Knizhnik-Zamolodchikov Equations and Lusztig's Isomorphisms.- L. Ehrenpreis: Hypergeometric Functions.- B.L. Feigin: Differential Operators on the Moduli Space of G-Bundles on Algebraic Curve and Lie Algebra Cohomologies.- I.M. Gelfand, M.M. Kapranov, A.V. Zelevinsky: Hypergeometric Functions, Toric Varieties and Newton Polyhedra.- A. Kirillov: On Some Properties of Robinson-Schensted Correspondence.- V. Lakshmibai : Standard Monomial Theory for Sp2n.- V. Lakshmibai, N. Reshetikhin: Quantum Deformations of SLn/B and its Schubert Varieties.- L. Lewin: Supernumary Polylogarithmic Ladders and Related Functional Equations.- H. Majima: Resurgent Equations and Stokes Multipliers for the Generalized Confluent Hypergeometric Differential Equations of the Second Order.- M.P. Malliavin, P. Malliavin: An Infinitesimally Quasi Invariant Measure on the Group of Diffeomorphisms of the Circle.- B.M. McCoy: The Chiral Potts Model: from Physics to Mathematics and back.- M. Noumi: Quantum Groups and q-Orthogonal Polynomials - Towards a realization of Askey-Wilson polynomials on SUq(2).- M. Okado, H. Yamane: R-Matrices with Gauge Parameters and Multi-Parameter Quantized Enveloping Algebras.- K. Takasaki: Analytic Expression of Voros Coefficients and its Application to WKB Connection Problem.- Programme.- List of Participants.

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Contents: T. Aoki, T. Kawai, Y. Takei: The Bender-Wu Analysis and the Voros Theory.- K. Aomoto, Y. Kato: A q-Analogue of de Rham Cohomology.- I. Cherednik: Affine Extensions of Knizhnik-Zamolodchikov Equations and Lusztig's Isomorphisms.- L. Ehrenpreis: Hypergeometric Functions.- B.L. Feigin: Differential Operators on the Moduli Space of G-Bundles on Algebraic Curve and Lie Algebra Cohomologies.- I.M. Gelfand, M.M. Kapranov, A.V. Zelevinsky: Hypergeometric Functions, Toric Varieties and Newton Polyhedra.- A. Kirillov: On Some Properties of Robinson-Schensted Correspondence.- V. Lakshmibai : Standard Monomial Theory for Sp2n.- V. Lakshmibai, N. Reshetikhin: Quantum Deformations of SLn/B and its Schubert Varieties.- L. Lewin: Supernumary Polylogarithmic Ladders and Related Functional Equations.- H. Majima: Resurgent Equations and Stokes Multipliers for the Generalized Confluent Hypergeometric Differential Equations of the Second Order.- M.P. Malliavin, P. Malliavin: An Infinitesimally Quasi Invariant Measure on the Group of Diffeomorphisms of the Circle.- B.M. McCoy: The Chiral Potts Model: from Physics to Mathematics and back.- M. Noumi: Quantum Groups and q-Orthogonal Polynomials - Towards a realization of Askey-Wilson polynomials on SUq(2).- M. Okado, H. Yamane: R-Matrices with Gauge Parameters and Multi-Parameter Quantized Enveloping Algebras.- K. Takasaki: Analytic Expression of Voros Coefficients and its Application to WKB Connection Problem.- Programme.- List of Participants.
Content:
Front Matter....Pages I-V
The Bender-Wu Analysis and the Voros Theory....Pages 1-29
A q-analogue of de Rham cohomology....Pages 30-62
Affine Extensions of Knizhnik-Zamolodchikov Equations and Lusztig’s Isomorphisms....Pages 63-77
Hypergeometric Functions....Pages 78-89
Differential operators on the moduli space of G-bundles on algebraic curve and Lie algebra cohomologies....Pages 90-103
Hypergeometric Functions, Toric Varieties and Newton Polyhedra....Pages 104-121
On Some Properties of Robinson-Schensted Correspondence....Pages 122-126
Standard Monomial Theory for ?p2n ....Pages 127-148
Quantum Deformations of SLn/B and its Schubert Varieties....Pages 149-168
Supernumary Polylogarithmic Ladders and Related Functional Equations....Pages 169-221
Resurgent Equations and Stokes Multipliers for the Generalized Confluent Hypergeometric Differential Equations of the Second Order....Pages 222-233
An Infinitesimally Quasi Invariant Measure on the Group of Diffeomorphisms of the Circle....Pages 234-244
The Chiral Potts Model: from Physics to Mathematics and back....Pages 245-259
Quantum Groups and q-Orthogonal Polynomials....Pages 260-288
R-matrices with gauge parameters and multi-parameter quantized enveloping algebras....Pages 289-293
Analytic Expression of Voros Coefficients and Its Application to WKB Connection Problem....Pages 294-315
Back Matter....Pages 316-318

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Contents: T. Aoki, T. Kawai, Y. Takei: The Bender-Wu Analysis and the Voros Theory.- K. Aomoto, Y. Kato: A q-Analogue of de Rham Cohomology.- I. Cherednik: Affine Extensions of Knizhnik-Zamolodchikov Equations and Lusztig's Isomorphisms.- L. Ehrenpreis: Hypergeometric Functions.- B.L. Feigin: Differential Operators on the Moduli Space of G-Bundles on Algebraic Curve and Lie Algebra Cohomologies.- I.M. Gelfand, M.M. Kapranov, A.V. Zelevinsky: Hypergeometric Functions, Toric Varieties and Newton Polyhedra.- A. Kirillov: On Some Properties of Robinson-Schensted Correspondence.- V. Lakshmibai : Standard Monomial Theory for Sp2n.- V. Lakshmibai, N. Reshetikhin: Quantum Deformations of SLn/B and its Schubert Varieties.- L. Lewin: Supernumary Polylogarithmic Ladders and Related Functional Equations.- H. Majima: Resurgent Equations and Stokes Multipliers for the Generalized Confluent Hypergeometric Differential Equations of the Second Order.- M.P. Malliavin, P. Malliavin: An Infinitesimally Quasi Invariant Measure on the Group of Diffeomorphisms of the Circle.- B.M. McCoy: The Chiral Potts Model: from Physics to Mathematics and back.- M. Noumi: Quantum Groups and q-Orthogonal Polynomials - Towards a realization of Askey-Wilson polynomials on SUq(2).- M. Okado, H. Yamane: R-Matrices with Gauge Parameters and Multi-Parameter Quantized Enveloping Algebras.- K. Takasaki: Analytic Expression of Voros Coefficients and its Application to WKB Connection Problem.- Programme.- List of Participants.
Content:
Front Matter....Pages I-V
The Bender-Wu Analysis and the Voros Theory....Pages 1-29
A q-analogue of de Rham cohomology....Pages 30-62
Affine Extensions of Knizhnik-Zamolodchikov Equations and Lusztig’s Isomorphisms....Pages 63-77
Hypergeometric Functions....Pages 78-89
Differential operators on the moduli space of G-bundles on algebraic curve and Lie algebra cohomologies....Pages 90-103
Hypergeometric Functions, Toric Varieties and Newton Polyhedra....Pages 104-121
On Some Properties of Robinson-Schensted Correspondence....Pages 122-126
Standard Monomial Theory for ?p2n ....Pages 127-148
Quantum Deformations of SLn/B and its Schubert Varieties....Pages 149-168
Supernumary Polylogarithmic Ladders and Related Functional Equations....Pages 169-221
Resurgent Equations and Stokes Multipliers for the Generalized Confluent Hypergeometric Differential Equations of the Second Order....Pages 222-233
An Infinitesimally Quasi Invariant Measure on the Group of Diffeomorphisms of the Circle....Pages 234-244
The Chiral Potts Model: from Physics to Mathematics and back....Pages 245-259
Quantum Groups and q-Orthogonal Polynomials....Pages 260-288
R-matrices with gauge parameters and multi-parameter quantized enveloping algebras....Pages 289-293
Analytic Expression of Voros Coefficients and Its Application to WKB Connection Problem....Pages 294-315
Back Matter....Pages 316-318
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