06356nam 22018015 450 991015475280332120190708092533.01-4008-8177-310.1515/9781400881772(CKB)3710000000620140(SSID)ssj0001651247(PQKBManifestationID)16426439(PQKBTitleCode)TC0001651247(PQKBWorkID)13700154(PQKB)10595664(MiAaPQ)EBC4738579(DE-B1597)467930(OCoLC)979746993(DE-B1597)9781400881772(EXLCZ)99371000000062014020190708d2016 fg engurcnu||||||||txtccrCharacters of Reductive Groups over a Finite Field. (AM-107), Volume 107 /George LusztigPrinceton, NJ : Princeton University Press, [2016]©19841 online resource (408 pages) illustrationsAnnals of Mathematics Studies ;278Bibliographic Level Mode of Issuance: Monograph0-691-08350-9 0-691-08351-7 Includes bibliographical references and indexes.Frontmatter -- TABLE OF CONTENTS -- INTRODUCTION -- 1. COMPUTATION OF LOCAL INTERSECTION COHOMOLOGY OF CERTAIN LINE BUNDLES OVER A SCHUBERT VARIETY -- 2. LOCAL INTERSECTION COHOMOLOGY WITH TWISTED COEFFICIENTS OF THE CLOSURES OF THE VARIETIES XW -- 3. GLOBAL INTERSECTION COHOMOLOGY WITH TWISTED COEFFICIENTS OF THE VARIETY X̅W -- 4. REPRESENTATIONS OF WEYL GROUPS -- 5. CELLS IN WEYL GROUPS -- 6. AN INTEGRALITY THEOREM AND A DISJOINTNESS THEOREM -- 7. SOME EXCEPTIONAL GROUPS -- 8. DECOMPOSITION OF INDUCED REPRESENTATIONS -- 9. CLASSICAL GROUPS -- 10. COMPLETION OF THE PROOF OF THEOREM 4.23 -- 11. EIGENVALUES OF FROBENIUS -- 12. ON THE STRUCTURE OF LEFT CELLS -- 13. RELATIONS WITH CONJUGACY CLASSES -- 14. CONCLUDING REMARKS -- APPENDIX -- REFERENCES -- SUBJECT INDEX -- NOTATION INDEX -- BackmatterThis book presents a classification of all (complex)irreducible representations of a reductive group withconnected centre, over a finite field. To achieve this,the author uses etale intersection cohomology, anddetailed information on representations of Weylgroups.Annals of mathematics studies ;Number 107.Finite groupsFinite fields (Algebra)Characters of groupsAddition.Algebra representation.Algebraic closure.Algebraic group.Algebraic variety.Algebraically closed field.Bijection.Borel subgroup.Cartan subalgebra.Character table.Character theory.Characteristic function (probability theory).Characteristic polynomial.Class function (algebra).Classical group.Coefficient.Cohomology with compact support.Cohomology.Combination.Complex number.Computation.Conjugacy class.Connected component (graph theory).Coxeter group.Cyclic group.Cyclotomic polynomial.David Kazhdan.Dense set.Derived category.Diagram (category theory).Dimension.Direct sum.Disjoint sets.Disjoint union.E6 (mathematics).Eigenvalues and eigenvectors.Endomorphism.Equivalence class.Equivalence relation.Existential quantification.Explicit formula.Explicit formulae (L-function).Fiber bundle.Finite field.Finite group.Fourier transform.Green's function.Group (mathematics).Group action.Group representation.Harish-Chandra.Hecke algebra.Identity element.Integer.Irreducible representation.Isomorphism class.Jordan decomposition.Line bundle.Linear combination.Local system.Mathematical induction.Maximal torus.Module (mathematics).Monodromy.Morphism.Orthonormal basis.P-adic number.Parametrization.Parity (mathematics).Partially ordered set.Perverse sheaf.Pointwise.Polynomial.Quantity.Rational point.Reductive group.Ree group.Schubert variety.Scientific notation.Semisimple Lie algebra.Sheaf (mathematics).Simple group.Simple module.Special case.Standard basis.Subset.Subtraction.Summation.Surjective function.Symmetric group.Tensor product.Theorem.Two-dimensional space.Unipotent representation.Vector bundle.Vector space.Verma module.Weil conjecture.Weyl group.Zariski topology.Finite groups.Finite fields (Algebra)Characters of groups.512/.2SK 260rvkLusztig George, 59231DE-B1597DE-B1597BOOK9910154752803321Characters of Reductive Groups over a Finite Field. (AM-107), Volume 1072788036UNINA