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catalog contributor b13045325.
catalog created "c2003.".
catalog date "2003".
catalog date "c2003.".
catalog dateCopyrighted "c2003.".
catalog description "Chapter 1. Hypergeometric Solutions of KZ Equations 1 -- 1.1. Examples of Hypergeometric Integrals 1 -- 1.2. Knizhnik-Zamolodchikov Equations 3 -- 1.3. Examples of Solutions 5 -- 1.4. Solutions of the KZ Equation with Values in Sing M[superscript multiply sign in circle m vertical bar m vertical bar -- 2k] 6 -- 1.5. Solutions of the KZ Equation with Values in Sing L[superscript multiply sign in circle m vertical bar m vertical bar -- 2k] 8 -- 1.6. The Classical Hypergeometric Series 8 -- 1.7. Identities for Differential Forms 10 -- 1.8. Hyperplane Arrangements 11 -- Chapter 2. Cycles of Integrals and the Monodromy of the KZ Equation 15 -- 2.1. Cycles for Solutions in Sing M[superscript multiply sign in circle m vertical bar m vertical bar -- 2] 15 -- 2.2. The Quantum Group U[subscript q](sl[subscript 2]) 18 -- 2.3. The Yang-Baxter Equation and Representations of Braid Groups 20 -- 2.4.".
catalog description "Coefficients f[superscript (k) subscript m, n] and Values of Macdonald Polynomials 80 -- 5.12. Modular Transformations of Elliptic Hypergeometric Functions 81 -- 5.13. Trace Functions for U[subscript q](sl[subscript 2]) 82 -- Chapter 6. q-Hypergeometric Solutions of qKZ Equations 85 -- 6.1. Quantum Knizhnik-Zamolodchikov Equations 85 -- 6.2. Quasi-Classical Asymptotics of Solutions and Eigenvectors 88 -- 6.3. An Example of Quantization of Hypergeometric Functions 89 -- 6.4. q-Hypergeometric Solutions, General Case 97 -- 6.5. The q-Hypergeometric Pairing 103 -- 6.6. Quantization of the Kohno-Drinfeld Theorem 105.".
catalog description "Critical Points of [Phi subscript k, n](t, z, m) if m[subscript 1] ..., m[subscript n] Are Natural Numbers 60 -- 4.7. Critical Points and Fuchsian Equations with Polynomial Solutions 62 -- 4.8. Resonant Local Systems 67 -- Chapter 5. Elliptic Hypergeometric Functions 69 -- 5.1. Knizhnik-Zamolodchikov-Bernard Equations 69 -- 5.2. The Case of n = 1 and V = L[subscript 2p] 70 -- 5.3. Quasi-Classical Asymptotics of Solutions to the KZB Heat Equation 71 -- 5.4. Elliptic Hypergeometric Functions Associated with One Marked Point 72 -- 5.5. Integral Representations for Elliptic Hypergeometric Functions 73 -- 5.6. Elliptic Selberg Integrals 74 -- 5.7. Transformations Acting on the Space of Conformal Blocks 75 -- 5.8. Relations Between Theta Functions 76 -- 5.9. Basic Relations Between Elliptic Hypergeometric Functions 77 -- 5.10. Macdonald Polynomials and the Shift Operator 79 -- 5.11.".
catalog description "Includes bibliographical references (p. 109-115) and index.".
catalog description "Quantum Singular Vectors 22 -- 2.5. The Monodromy of KZ Equations 23 -- 2.6. A Remark on Integration Cycles 29 -- Chapter 3. Selberg Integral, Determinant Formulas, and Dynamical Equations 31 -- 3.1. The Selberg Integral 31 -- 3.2. A Connection with Finite Reflection Groups 32 -- 3.3. An Example of a Determinant Formula 33 -- 3.4. The Determinant Formula for Solutions in a Weight Subspace 36 -- 3.5. General Determinant Formulas 38 -- 3.6. Resonances 40 -- 3.7. Dynamical Equations 43 -- Chapter 4. Critical Points of Master Functions and the Bethe Ansatz 49 -- 4.1. The Gaudin Model and the Bethe Ansatz 49 -- 4.2. Asymptotic Solutions and Eigenvectors 50 -- 4.3. Quasi-Classical Asymptotics of Solutions to the KZ Equation 53 -- 4.4. The Shapovalov Norm of Bethe Vectors 56 -- 4.5. The Number of Critical Points of a Product of Powers of Linear Functions 58 -- 4.6.".
catalog extent "viii, 118 p. ;".
catalog identifier "0821828673 (alk. paper)".
catalog isPartOf "CBMS regional conference series in mathematics, 0160-7642 ; no. 98".
catalog isPartOf "Regional conference series in mathematics ; no. 98.".
catalog issued "2003".
catalog issued "c2003.".
catalog language "eng".
catalog publisher "Providence, R.I. : American Mathematical Society,".
catalog subject "510 s 515/.5 22".
catalog subject "Functions, Special Congresses.".
catalog subject "Knizhnik-Zamoldchikov equations Congresses.".
catalog subject "Knizhnik-Zamolodchikov equations Congresses.".
catalog subject "QA1 .R33 no. 98 QA351".
catalog subject "Representations of groups Congresses.".
catalog tableOfContents "Chapter 1. Hypergeometric Solutions of KZ Equations 1 -- 1.1. Examples of Hypergeometric Integrals 1 -- 1.2. Knizhnik-Zamolodchikov Equations 3 -- 1.3. Examples of Solutions 5 -- 1.4. Solutions of the KZ Equation with Values in Sing M[superscript multiply sign in circle m vertical bar m vertical bar -- 2k] 6 -- 1.5. Solutions of the KZ Equation with Values in Sing L[superscript multiply sign in circle m vertical bar m vertical bar -- 2k] 8 -- 1.6. The Classical Hypergeometric Series 8 -- 1.7. Identities for Differential Forms 10 -- 1.8. Hyperplane Arrangements 11 -- Chapter 2. Cycles of Integrals and the Monodromy of the KZ Equation 15 -- 2.1. Cycles for Solutions in Sing M[superscript multiply sign in circle m vertical bar m vertical bar -- 2] 15 -- 2.2. The Quantum Group U[subscript q](sl[subscript 2]) 18 -- 2.3. The Yang-Baxter Equation and Representations of Braid Groups 20 -- 2.4.".
catalog tableOfContents "Coefficients f[superscript (k) subscript m, n] and Values of Macdonald Polynomials 80 -- 5.12. Modular Transformations of Elliptic Hypergeometric Functions 81 -- 5.13. Trace Functions for U[subscript q](sl[subscript 2]) 82 -- Chapter 6. q-Hypergeometric Solutions of qKZ Equations 85 -- 6.1. Quantum Knizhnik-Zamolodchikov Equations 85 -- 6.2. Quasi-Classical Asymptotics of Solutions and Eigenvectors 88 -- 6.3. An Example of Quantization of Hypergeometric Functions 89 -- 6.4. q-Hypergeometric Solutions, General Case 97 -- 6.5. The q-Hypergeometric Pairing 103 -- 6.6. Quantization of the Kohno-Drinfeld Theorem 105.".
catalog tableOfContents "Critical Points of [Phi subscript k, n](t, z, m) if m[subscript 1] ..., m[subscript n] Are Natural Numbers 60 -- 4.7. Critical Points and Fuchsian Equations with Polynomial Solutions 62 -- 4.8. Resonant Local Systems 67 -- Chapter 5. Elliptic Hypergeometric Functions 69 -- 5.1. Knizhnik-Zamolodchikov-Bernard Equations 69 -- 5.2. The Case of n = 1 and V = L[subscript 2p] 70 -- 5.3. Quasi-Classical Asymptotics of Solutions to the KZB Heat Equation 71 -- 5.4. Elliptic Hypergeometric Functions Associated with One Marked Point 72 -- 5.5. Integral Representations for Elliptic Hypergeometric Functions 73 -- 5.6. Elliptic Selberg Integrals 74 -- 5.7. Transformations Acting on the Space of Conformal Blocks 75 -- 5.8. Relations Between Theta Functions 76 -- 5.9. Basic Relations Between Elliptic Hypergeometric Functions 77 -- 5.10. Macdonald Polynomials and the Shift Operator 79 -- 5.11.".
catalog tableOfContents "Quantum Singular Vectors 22 -- 2.5. The Monodromy of KZ Equations 23 -- 2.6. A Remark on Integration Cycles 29 -- Chapter 3. Selberg Integral, Determinant Formulas, and Dynamical Equations 31 -- 3.1. The Selberg Integral 31 -- 3.2. A Connection with Finite Reflection Groups 32 -- 3.3. An Example of a Determinant Formula 33 -- 3.4. The Determinant Formula for Solutions in a Weight Subspace 36 -- 3.5. General Determinant Formulas 38 -- 3.6. Resonances 40 -- 3.7. Dynamical Equations 43 -- Chapter 4. Critical Points of Master Functions and the Bethe Ansatz 49 -- 4.1. The Gaudin Model and the Bethe Ansatz 49 -- 4.2. Asymptotic Solutions and Eigenvectors 50 -- 4.3. Quasi-Classical Asymptotics of Solutions to the KZ Equation 53 -- 4.4. The Shapovalov Norm of Bethe Vectors 56 -- 4.5. The Number of Critical Points of a Product of Powers of Linear Functions 58 -- 4.6.".
catalog title "Special functions, KZ type equations, and representation theory / Alexander Varchenko.".
catalog type "Conference proceedings. fast".
catalog type "text".