**Proceedings of Symposia in Pure Mathematics**

Volume: 49;
1989;
728 pp;
Hardcover

MSC: Primary 11;
Secondary 00; 14

Print ISBN: 978-0-8218-1483-3

Product Code: PSPUM/49.1

List Price: $139.00

AMS Member Price: $111.20

MAA Member Price: $125.10

**Electronic ISBN: 978-0-8218-9344-9
Product Code: PSPUM/49.1.E**

List Price: $139.00

AMS Member Price: $111.20

MAA Member Price: $125.10

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# Theta Functions–Bowdoin 1987, Part 1

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*Robert C. Gunning; Leon Ehrenpreis*

# Table of Contents

## Theta Functions-Bowdoin 1987, Part 1

- Contents iii4 free
- Preface ix10 free
- Infinite Analysis 112 free
- Systems of linear differential equations of infinite order: an aspect of infinite analysis 314
- A particular partition of unity: an auxiliary tool in Hodge theory 1930
- Is there an infinite-dimensional algebraic geometry? Hints from KDV 2738
- A correspondence between an infinite Grassmannian and arbitrary vector bundles on algebraic curves 3950
- The KP hierarchy and infinite-dimensional Grassmann manifolds 5162

- Integrable Systems 6778
- Some geometrical techniques in integrable systems 6980
- Generalized theta functions and homoclinic varieties 8798
- Explicit equations for the KP and MKP hierarchies 101112
- Introduction to algebraic integrable systems and their Painlevé analysis 107118
- Polynomial τ-functions for the AKNS hierarchy 133144
- Integrable systems as deformations of D-modules 143154

- Kac-Moody Algebras 169180
- The infinite wedge representation and the reciprocity law for algebraic curves 171182
- Exceptional hierarchies of soliton equations 191202
- Unitary representations of some infinite-dimensional Lie algebras 239250
- On highest weight and Fock space representations of the Virasoro algebra 259270
- Modular forms, strings, and ghosts 273284

- Lattice Models 285296
- Solution of Hirota's discrete-time Toda lattice equation and the critical correlations in the Z-invariant Ising model 287298
- Solvable lattice models 295306
- Theta function identities in a series of solvable lattice models 333344
- Star-triangle equations, quantum Lax pairs, and higher genus curves 341352
- Introduction to exactly solvable models in statistical mechanics 355366

- Physics 377388
- Jacobian Varieties 457468
- Schottky-Jung theory 459470
- Schottky relations on 1/2{C - C) 485496
- Analytic identities for theta functions 503514
- Translation manifolds and the Schottky problem 517528
- Mappings of closed Riemann surfaces 531542
- Geometric characterization of Jacobians and the Schottky equations 541552
- Vector bundles over curves and solutions of the KP equations 553564
- Deformations of singular points on theta divisors 571582
- Uniformization, local index theorem, and geometry of the moduli spaces of Riemann surfaces and vector bundles 581592
- Explicit actions of the theta groups for theta divisors on Jacobian surfaces 597608

- Prym Varieties 605616
- Algebraic Geometry 647658