Archimedean Zeta Integrals for GL(3) Times GL(2).

Cover
Title page
Introduction
Acknowledgments
Part 1. Whittaker functions
Chapter 1. Basic objects
1.1. Notation
1.2. Groups and algebras
1.3. Whittaker functions
1.4. Capelli elements
1.5. The gamma function and the Bessel functions
1.6. Special functions of two variables
Chapter 2. Preliminaries for ( ,\bR)
2.1. Generalized principal series representations
2.2. The elements of \g_{\bC} and (\g_{\bC})
2.3. The eigenvalues of generators of (\g_{\bC})
Chapter 3. Whittaker functions on (2,\bR)
3.1. Representations of (2)
3.2. Principal series representations
3.3. Principal series Whittaker functions
3.4. Essentially discrete series Whittaker functions
Chapter 4. Whittaker functions on (3,\bR)
4.1. Representations of (3)
4.2. Principal series representations
4.3. Principal series Whittaker functions at scalar -types
4.4. Principal series Whittaker functions at 3 dimensional -types
4.5. Generalized principal series representations
4.6. Generalized principal series Whittaker functions
Chapter 5. Preliminaries for ( ,\bC)
5.1. Principal series representations
5.2. The elements of \g_{\bC} and (\g_{\bC})
5.3. The eigenvalues of generators of (\g_{\bC})
Chapter 6. Whittaker functions on (2,\bC)
6.1. Representations of (2)
6.2. Principal series representations
6.3. Principal series Whittaker functions
Chapter 7. Whittaker functions on (3,\bC)
7.1. Representations of (3)
7.2. Principal series representations
7.3. Principal series Whittaker functions
Part 2. Archimedean zeta integrals for (3)× (2)
Chapter 8. Preliminaries
8.1. The aim of Part 2
8.2. Some formulas for the calculation
Chapter 9. The local zeta integrals for (3,\bR)× (2,\bR)
9.1. The local Langlands correspondence for ( ,\bR).

9.2. Preparations for (2)-modules
9.3. Whittaker functions on (2,\bR)
9.4. Whittaker functions on (3,\bR)
9.5. The local zeta integrals for (3,\bR)× (2,\bR)
9.6. The calculation for '= _{( ₁', ₂')}⊠ _{( ₂', ₂')}
9.7. The calculation for '= _{( ₁',1)}⊠ _{( ₂',0)}
9.8. The calculation for '= _{( ', ')}
Chapter 10. The local zeta integrals for (3,\bC)× (2,\bC)
10.1. The local Langlands correspondence for ( ,\bC)
10.2. Preparations for (2)-modules
10.3. Whittaker functions on (2,\bC)
10.4. Whittaker functions on (3,\bC)
10.5. The local zeta integrals for (3,\bC)× (2,\bC)
10.6. The calculation in the case ₂>
- ₂'
10.7. The calculation in the case - ₁'>
₂
10.8. The calculation in the case - ₂'≥ ₂ ₂₂₆₅ - ₁'
Appendix A. Archimedean zeta integrals for (2)× ( ) ( =1,2)
A.1. The local zeta integrals for (2,\bR)× (1,\bR)
A.2. The local zeta integrals for (2,\bR)× (2,\bR)
A.3. The local zeta integrals for (2,\bC)× (1,\bC)
A.4. The local zeta integrals for (2,\bC)× (2,\bC)
Bibliography
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