LEADER 05981nam 22015375 450 001 9910154750803321 005 20190708092533.0 010 $a1-4008-8249-4 024 7 $a10.1515/9781400882496 035 $a(CKB)3710000000622804 035 $a(MiAaPQ)EBC4738792 035 $a(DE-B1597)467956 035 $a(OCoLC)979836554 035 $a(DE-B1597)9781400882496 035 $a(EXLCZ)993710000000622804 100 $a20190708d2016 fg 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 14$aThe Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129 /$fC. Bushnell, P. C. Kutzko 210 1$aPrinceton, NJ : $cPrinceton University Press, $d[2016] 210 4$dİ1993 215 $a1 online resource (327 pages) $cillustrations 225 0 $aAnnals of Mathematics Studies ;$v311 311 $a0-691-02114-7 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tContents -- $tIntroduction -- $tComments for the reader -- $t1. Exactness and intertwining -- $t2. The structure of simple strata -- $t3. The simple characters of a simple stratum -- $t4. Interlude with Hecke algebra -- $t5. Simple types -- $t6. Maximal types -- $t7. Typical representations -- $t8. Atypical representations -- $tReferences -- $tIndex of notation and terminology 330 $aThis work gives a full description of a method for analyzing the admissible complex representations of the general linear group G = Gl(N,F) of a non-Archimedean local field F in terms of the structure of these representations when they are restricted to certain compact open subgroups of G. The authors define a family of representations of these compact open subgroups, which they call simple types. The first example of a simple type, the "trivial type," is the trivial character of an Iwahori subgroup of G. The irreducible representations of G containing the trivial simple type are classified by the simple modules over a classical affine Hecke algebra. Via an isomorphism of Hecke algebras, this classification is transferred to the irreducible representations of G containing a given simple type. This leads to a complete classification of the irreduc-ible smooth representations of G, including an explicit description of the supercuspidal representations as induced representations. A special feature of this work is its virtually complete reliance on algebraic methods of a ring-theoretic kind. A full and accessible account of these methods is given here. 410 0$aAnnals of mathematics studies ;$vno. 129. 606 $aRepresentations of groups 606 $aNonstandard mathematical analysis 610 $aAbelian group. 610 $aAbuse of notation. 610 $aAdditive group. 610 $aAffine Hecke algebra. 610 $aAlgebra homomorphism. 610 $aApproximation. 610 $aAutomorphism. 610 $aBijection. 610 $aBlock matrix. 610 $aCalculation. 610 $aCardinality. 610 $aClassical group. 610 $aComputation. 610 $aConjecture. 610 $aConjugacy class. 610 $aContradiction. 610 $aCorollary. 610 $aCoset. 610 $aCritical exponent. 610 $aDiagonal matrix. 610 $aDimension (vector space). 610 $aDimension. 610 $aDiscrete series representation. 610 $aDiscrete valuation ring. 610 $aDivisor. 610 $aEigenvalues and eigenvectors. 610 $aEquivalence class. 610 $aExact sequence. 610 $aExactness. 610 $aExistential quantification. 610 $aExplicit formula. 610 $aExplicit formulae (L-function). 610 $aField extension. 610 $aFinite group. 610 $aFunctor. 610 $aGauss sum. 610 $aGeneral linear group. 610 $aGroup theory. 610 $aHaar measure. 610 $aHarmonic analysis. 610 $aHecke algebra. 610 $aHomomorphism. 610 $aIdentity matrix. 610 $aInduced representation. 610 $aInteger. 610 $aIrreducible representation. 610 $aIsomorphism class. 610 $aIwahori subgroup. 610 $aJordan normal form. 610 $aLevi decomposition. 610 $aLocal Langlands conjectures. 610 $aLocal field. 610 $aLocally compact group. 610 $aMathematics. 610 $aMatrix coefficient. 610 $aMaximal compact subgroup. 610 $aMaximal ideal. 610 $aMultiset. 610 $aNormal subgroup. 610 $aP-adic number. 610 $aPermutation matrix. 610 $aPolynomial. 610 $aProfinite group. 610 $aQuantity. 610 $aRational number. 610 $aReductive group. 610 $aRepresentation theory. 610 $aRequirement. 610 $aResidue field. 610 $aRing (mathematics). 610 $aScientific notation. 610 $aSimple module. 610 $aSpecial case. 610 $aSub"ient. 610 $aSubgroup. 610 $aSubset. 610 $aSupport (mathematics). 610 $aSymmetric group. 610 $aTensor product. 610 $aTerminology. 610 $aTheorem. 610 $aTopological group. 610 $aTopology. 610 $aVector space. 610 $aWeil group. 610 $aWeyl group. 615 0$aRepresentations of groups. 615 0$aNonstandard mathematical analysis. 676 $a512/.2 686 $aSK 340$2rvk 700 $aBushnell$b C., $01126189 702 $aKutzko$b P. C., 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910154750803321 996 $aThe Admissible Dual of GL(N) via Compact Open Subgroups. (AM-129), Volume 129$92657528 997 $aUNINA