Subregular Germ of Orbital Integrals.

Intro -- Contents -- Introduction -- I. Basic Constructions -- 1. Background Information -- 2. The Igusa Variety -- 3. The Variety S[sup(0)] -- 4. The Morphism S[sub(1)] → S -- 5. Cocycles -- 6. The Data -- II. Coordinates and Coordinate Relations -- 1. The Coordinates x(W,(β) -- 2. The Coordinates ω(β) -- 3. The Extension of ω(β) to Y -- 4. The Coordinate Ring -- 5. A Computation of t[sup(-1)]n[sup(-1)]tn -- 6. A Technical Lemma -- 7. Application to G[sub(2)] -- 8. The Functions n[sub(γ)] -- 9. The Fundamental Divisors on Y[sub(Γ)] -- III. Groups of Rank Two -- 1. Zero Patterns -- 2. Coordinate Relations -- 3. Exclusion of Spurious Divisors (rank two) -- IV. The Subregular Spurious Divisor -- 1. Subregular Unipotent Conjugacy Classes -- 2. Exclusion of Spurious Divisors -- 3. The graph Γ[sub(0)] -- 4. The Modified Star -- 5. Weyl Chambers -- 6. A Lemma about Cells -- 7. Contact -- 8. Assumption 3.1 -- V. The Subregular Fundamental Divisor -- 1. Regularity -- 2. Igusa Theory and Measures -- 3. Principal Value Integrals at Points of E[sub(α)] ∩ E[sub(β)] -- 4. Igusa Data for Interchanged Divisors -- 5. Transition Functions -- 6. Coordinate Relations -- VI. Rationality and Characters -- 1. Rationality -- 2. The Characters k(E[sub(α)]) -- 3. m[sub(k)](e) and the Vanishing of Integrals -- VII. Applications to Endoscopic Groups -- 1. Endoscopic Groups -- 2. Characters, Centers, and Endoscopic Groups -- 3. Compatibility of Characters -- 4. Stable Orbital Integrals -- 5. Unitary Groups -- References -- Notation and Conventions.

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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.