06204nam 22017055 450 991015474720332120190708092533.01-4008-8244-310.1515/9781400882441(CKB)3710000000627782(SSID)ssj0001651235(PQKBManifestationID)16426438(PQKBTitleCode)TC0001651235(PQKBWorkID)12978091(PQKB)11680870(MiAaPQ)EBC4738726(DE-B1597)467935(OCoLC)979747114(DE-B1597)9781400882441(EXLCZ)99371000000062778220190708d2016 fg engurcnu||||||||txtccrAutomorphic Representation of Unitary Groups in Three Variables. (AM-123), Volume 123 /Jonathan David RogawskiPrinceton, NJ : Princeton University Press, [2016]©19911 online resource (273 pages)Annals of Mathematics Studies ;306Bibliographic Level Mode of Issuance: Monograph0-691-08586-2 0-691-08587-0 Includes bibliographical references and indexes.Frontmatter -- Introduction -- Chapter 1. Preliminary definitions and notation -- Chapter 2. The trace formula -- Chapter 3. Stable conjugacy -- Chapter 4. Orbital integrals and endoscopic groups -- Chapter 5. Stabilization -- Chapter 6. Weighted orbital integrals -- Chapter 7. Elliptic singular terms -- Chapter 8. Germ expansions and limit formulas -- Chapter 9. Singularities -- Chapter 10. The stable trace formula -- Chapter 11. The Unitary group in two variables -- Chapter 12. Representation theory -- Chapter 13. Automorphic representations -- Chapter 14. Comparison of inner forms -- Chapter 15. Additional results -- References -- Subject Index -- Notation IndexThe purpose of this book is to develop the stable trace formula for unitary groups in three variables. The stable trace formula is then applied to obtain a classification of automorphic representations. This work represents the first case in which the stable trace formula has been worked out beyond the case of SL (2) and related groups. Many phenomena which will appear in the general case present themselves already for these unitary groups.Annals of mathematics studies ;no. 123.Unitary groupsTrace formulasRepresentations of groupsAutomorphic formsAbelian group.Abuse of notation.Addition.Admissible representation.Algebraic closure.Algebraic group.Algebraic number field.Asymptotic expansion.Automorphism.Base change map.Base change.Bijection.Borel subgroup.Cartan subgroup.Class function (algebra).Coefficient.Combination.Compact group.Complementary series representation.Complex number.Congruence subgroup.Conjugacy class.Continuous function.Corollary.Countable set.Diagram (category theory).Differential operator.Dimension (vector space).Dimension.Discrete spectrum.Division algebra.Division by zero.Eigenvalues and eigenvectors.Embedding.Equation.Existential quantification.Finite set.Fourier transform.Fundamental lemma (Langlands program).G factor (psychometrics).Galois group.Global field.Haar measure.Hecke algebra.Homomorphism.Hyperbolic set.Index notation.Irreducible representation.Isomorphism class.L-function.Langlands classification.Linear combination.Local field.Mathematical induction.Maximal compact subgroup.Maximal torus.Morphism.Multiplicative group.Neighbourhood (mathematics).Orbital integral.Oscillator representation.P-adic number.Parity (mathematics).Principal series representation.Quaternion algebra.Quaternion.Reductive group.Regular element.Remainder.Representation theory.Ring of integers.Scientific notation.Semisimple algebra.Set (mathematics).Shimura variety.Simple algebra.Smoothness.Special case.Stable distribution.Subgroup.Summation.Support (mathematics).Tate conjecture.Tensor product.Theorem.Trace formula.Triangular matrix.Unitary group.Variable (mathematics).Weight function.Weil group.Unitary groups.Trace formulas.Representations of groups.Automorphic forms.512/.2Rogawski Jonathan David, 59388DE-B1597DE-B1597BOOK9910154747203321Automorphic Representation of Unitary Groups in Three Variables. (AM-123), Volume 1232788677UNINA