The subregular germ of orbital integrals / Thomas C. Hales.

Format:

Book

Author/Creator:

Hales, Thomas Callister, author.

Series:

Memoirs of the American Mathematical Society ; Volume 99, Number 476.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 99, Number 476

Language:

English

Subjects (All):

p-adic fields.

Representations of groups.

Germs (Mathematics).

Physical Description:

1 online resource (161 p.)

Edition:

1st ed.

Other Title:

Orbital integrals.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 1992.

Language Note:

English

Summary:

Langlands theory predicts deep relationships between representations of different reductive groups over a local or global field. The trace formula attempts to reduce many such relationships to problems concerning conjugacy classes and integrals over conjugacy classes (orbital integrals) on p-acid groups. It is possible to reformulate these problems as ones in algebraic geometry by associating a variety Y to each reductive group. Using methods of Igusa, the geometrical properties of the variety give detailed information about the asymptotic behaviour of integrals over conjugacy classes. This monograph constructs the variety Y and describes its geometry. As an application, the author uses the variety to give formulas for the leading terms (regular and subregular germs) in the asymptotic expansion of orbital integrals over p-acid fields. The final chapter shows how the properties of the variety may be used to confirm some predictions of Langlands theory on orbital integrals, Shalika germs, and endoscopy.

Contents:

""Contents""; ""Introduction""; ""I. Basic Constructions""; ""1. Background Information""; ""2. The Igusa Variety""; ""3. The Variety S[sup(0)]""; ""4. The Morphism S[sub(1)] â?? S""; ""5. Cocycles""; ""6. The Data""; ""II. Coordinates and Coordinate Relations""; ""1. The Coordinates x(W,(β)""; ""2. The Coordinates Ï?(β)""; ""3. The Extension of Ï?(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(Î?)]""

""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 Î?[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)] â?© 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""

Notes:

"September 1992, volume 99, number 476 (third of 4 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0902-X