Handel, Messiah / Donald Burrows.

Format:

Book

Author/Creator:

Burrows, Donald, 1945- author.

Contributor:

American Council of Learned Societies.

Series:

Cambridge music handbooks.

Cambridge music handbooks

Language:

English

Subjects (All):

Handel, George Frideric, 1685-1759. Messiah.

Handel, George Frideric.

Physical Description:

1 online resource (x, 127 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 1991.

Language Note:

English

Summary:

This new guide to Handel's most celebrated work traces the course of Messiah from Handel's initial musical response to the libretto, through the oratorio's turbulent first years to its eventual popularity with the Foundling Hospital performances. Different chapters consider the varying reception the work received in Dublin and London, the uneasy relationship between the composer and his librettist Charles Jennens and the many changes Messiah underwent through the varying needs and capacities of Handel's performers. As well as tracing the history of the work's development, the book addresses musical and technical issues such as Messiah's place in the oratorio genre, Handel's treatment of structural design, tonal relationships and English word-setting. An edited libretto elucidates the variants between the text that Handel set and the texts of the early printed word-books. Donald Burrows brings many new insights to this fascinating account of one of the favourite works of the concert hall.

Contents:

Cover

Frontmatter

Contents

Preface

Finite and affine reflection groups

Finite reflection groups

1.1 Reflections

1.2 Roots

1.3 Positive and simple systems

1.4 Conjugacy of positive and simple systems

1.5 Generation by simple reflections

1.6 The length function

1.7 Deletion and Exchange Conditions

1.8 Simple transitivity and the longest element

1.9 Generators and relations

1.10 Parabolic subgroups

1.11 Poincaré polynomials

1.12 Fundamental domains

1.13 The lattice of parabolic subgroups

1.14 Reflections in W

1.15 The Coxeter complex

1.16 An alternating sum formula

Classification of finite reflection groups

2.1 Isomorphisms

2.2 Irreducible components

2.3 Coxeter graphs and associated bilinear forms

2.4 Some positive definite graphs

2.5 Some positive semidefinite graphs

2.6 Subgraphs

2.7 Classification of graphs of positive type

2.8 Crystallographic groups

2.9 Crystallographic root systems and Weyl groups

2.10 Construction of root systems

2.11 Computing the order of W

2.12 Exceptional Weyl groups

2.13 Groups of types H3 and H4

Polynomial invariants of finite reflection groups

3.1 Polynomial invariants of a finite group

3.2 Finite generation

3.3 A divisibility criterion

3.4 The key lemma

3.5 Chevalley's Theorem

3.6 The module of covariants

3.7 Uniqueness of the degrees

3.8 Eigenvalues

3.9 Sum and product of the degrees

3.10 Jacobian criterion for algebraic independence

3.11 Groups with free rings of invariants

3.12 Examples

3.13 Factorization of the Jacobian

3.14 Induction and restriction of class functions

3.15 Factorization of the Poincaré polynomial

3.16 Coxeter elements

3.17 Action on a plane

3.18 The Coxeter number

3.19 Eigenvalues of Coxeter elements.

3.20 Exponents and degrees of Weyl groups

Affine reflection groups

4.1 Affine reflections

4.2 Affine Weyl groups

4.3 Alcoves

4.4 Counting hyperplanes

4.5 Simple transitivity

4.6 Exchange Condition

4.7 Coxeter graphs and extended Dynkin diagrams

4.8 Fundamental domain

4.9 A formula for the order of W

4.10 Groups generated by affine reflections

General theory of Coxeter groups

Coxeter groups

5.1 Coxeter systems

5.2 Length function

5.3 Geometric representation of W

5.4 Positive and negative roots

5.5 Parabolic subgroups

5.6 Geometric interpretation of the length function

5.7 Roots and reflections

5.8 Strong Exchange Condition

5.9 Bruhat ordering

5.10 Subexpressions

5.11 Intervals in the Bruhat ordering

5.12 Poincaré series

5.13 Fundamental domain for W

Special cases

6.1 Irreducible Coxeter systems

6.2 More on the geometric representation

6.3 Radical of the bilinear form

6.4 Finite Coxeter groups

6.5 Affine Coxeter groups

6.6 Crystallographic Coxeter groups

6.7 Coxeter groups of rank 3

6.8 Hyperbolic Coxeter groups

6.9 List of hyperbolic Coxeter groups

Hecke algebras and Kazhdan-Lusztig polynomials

7.1 Generic algebras

7.2 Commuting operators

7.3 Conclusion of the proof

7.4 Hecke algebras and inverses

7.5 Computing the R-polynomials

7.6 Special case: finite Coxeter groups

7.7 An involution on H

7.8 Further properties of R-polynomials

7.9 Kazhdan-Lusztig polynomials

7.10 Uniqueness

7.11 Existence

7.12 Examples

7.13 Inverse Kazhdan-Lusztig polynomials

7.14 Multiplication formulas

7.15 Cells and representations of Hecke algebras

Complements

8.1 The Word Problem

8.2 Reflection subgroups

8.3 Involutions

8.4 Coxeter elements and their eigenvalues

8.5 Möbius function of the Bruhat ordering.

8.6 Intervals and Bruhat graphs

8.7 Shellability

8.8 Automorphisms of the Bruhat ordering

8.9 Poincaré series of affine Weyl groups

8.10 Representations of finite Coxeter groups

8.11 Schur multipliers

8.12 Coxeter groups and Lie theory

References

Index.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 121-122) and index.

ISBN:

9781139085557

1139085557

9780511620096

0511620098

OCLC:

935276806

Publisher Number:

2027/heb07576 hdl