Ebook: Symmetric Functions 2001: Surveys of Developments and Perspectives

This book surveys recent developments and outlines research prospects in various fields, the fundamental questions of which can be stated in the language of symmetric functions. Interdisciplinary interconnections are emphasized.

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This book surveys recent developments and outlines research prospects in various fields, the fundamental questions of which can be stated in the language of symmetric functions. Interdisciplinary interconnections are emphasized.
Content:
Front Matter....Pages i-xiii
Notes on Macdonald Polynomials and the Geometry of Hilbert Schemes....Pages 1-64
The Laplacian Method....Pages 65-91
Kerov’s Central Limit Theorem for the Plancherel Measure on Young Diagrams....Pages 93-151
Symmetric Functions and the Fock Space....Pages 153-177
An Introduction to Birational Weyl Group Actions....Pages 179-222
Symmetric Functions and Random Partitions....Pages 223-252
From Littlewood-Richardson Coefficients to Cluster Algebras in Three Lectures....Pages 253-273

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This book surveys recent developments and outlines research prospects in various fields, the fundamental questions of which can be stated in the language of symmetric functions. Interdisciplinary interconnections are emphasized.
Content:
Front Matter....Pages i-xiii
Notes on Macdonald Polynomials and the Geometry of Hilbert Schemes....Pages 1-64
The Laplacian Method....Pages 65-91
Kerov’s Central Limit Theorem for the Plancherel Measure on Young Diagrams....Pages 93-151
Symmetric Functions and the Fock Space....Pages 153-177
An Introduction to Birational Weyl Group Actions....Pages 179-222
Symmetric Functions and Random Partitions....Pages 223-252
From Littlewood-Richardson Coefficients to Cluster Algebras in Three Lectures....Pages 253-273
....