Representation Theory of Real Reductive Lie Groups.

Intro -- Contents -- Preface -- Guide to the Atlas Software: Computational Representation Theory of Real Reductive Groups -- Problems for Real Groups -- 1. Endoscopic transfer -- 2. Endoscopic character identities -- 3. Orthogonality relations -- 4. Weighted orbital integrals -- 5. Intertwining operators and residues -- 6. Twisted groups -- 7. Trace identities for intertwining operators -- 8. Construction of A-packets -- 9. Properties of A-packets -- 10. Functorial transfer -- References -- Unitarizable Minimal Principal Series of Reductive Groups -- 1. Introduction -- 2. Minimal principal series for real groups -- 3. Graded Hecke algebra and p-adic groups -- 4. Petite K-types for split real groups -- 5. Spherical unitary dual -- 6. Lists of unitary spherical parameters -- References -- Computations in Real Tori -- Weighted Orbital Integrals -- Introduction to Endoscopy -- 1. Introduction -- 1.1. What is endoscopy about? -- 1.2. The contents of these lectures -- 2. Some basic definitions -- 2.1. Orbital integrals -- 2.2. Pseudo-coefficients for discrete series -- 2.3. Stable conjugacy -- 2.4. L-packets -- 2.5. Arthur packets -- 2.6. The Weil and the Langlands groups -- 2.7. L-groups and Langlands parameters -- 3. GL(2) -- 3.1. Representations of GL(2,R) -- 3.2. Langlands parameters for G L(2, R) -- 3.3. Endoscopy for GL(2, F) -- 4. SL(2) -- 4.1. Endoscopy for SL(2, R) -- 4.2. Representations of SL(2, R) -- 4.3. Langlands parameters for SL(2, R) -- 4.4. Character identities -- 4.5. Asymptotic behaviour of orbital integrals and geometric transfer -- 5. U(2, 1) -- 5.1. Endoscopy for U(2, 1) -- 5.2. Discrete series and transfer for U(2, 1) -- 5.3. The dual picture for U(2, 1) -- 6. Galois cohomology and Endoscopy -- 6.1. Non abelian hypercohomology -- 6.2. Galois cohomology and abelianized cohomology -- 6.3. Stable conjugacy and k-orbital integrals.

6.4. Stable conjugacy and compact Cartan subgroups over R -- 6.5. Endoscopic groups -- 6.6. The dual picture -- 6.7. Endoscopic transfer -- 7. Discrete series and endoscopy -- 7.1. L-packets of discrete series over R -- 7.2. General Discrete transfer -- 8. Further developments -- 8.1. K-groups -- 8.2. The twisted case -- 8.3. Trace formula stabilization -- 9. Bibliography -- Tempered Endoscopy for Real Groups I: Geometric Transfer with Canonical Factors.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.