03509nam 2200577 450 991048075660332120170822123721.01-4704-0524-5(CKB)3360000000465102(EBL)3114124(SSID)ssj0000889189(PQKBManifestationID)11497178(PQKBTitleCode)TC0000889189(PQKBWorkID)10876187(PQKB)11282699(MiAaPQ)EBC3114124(PPN)195418077(EXLCZ)99336000000046510220080709h20082008 uy| 0engur|n|---|||||txtccrRepresentations of shifted Yangians and finite W-algebras /Jonathan Brundan, Alexander KleshchevProvidence, Rhode Island :American Mathematical Society,[2008]©20081 online resource (122 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 918"November 2008, volume 196, number 918 (end of volume)."0-8218-4216-1 Includes bibliographical references (pages 105-107).""Contents""; ""Chapter 1. Introduction""; ""Acknowledgements""; ""Chapter 2. Shifted Yangians""; ""2.1. Generators and relations""; ""2.2. PBW theorem""; ""2.3. Some automorphisms""; ""2.4. Parabolic generators""; ""2.5. Hopf algebra structure""; ""2.6. The center of Y[sub(n)](Ï?)""; ""Chapter 3. Finite W-algebras""; ""3.1. Pyramids""; ""3.2. Finite W-algebras""; ""3.3. Invariants""; ""3.4. Finite W-algebras are quotients of shifted Yangians""; ""3.5. More automorphisms""; ""3.6. Miura transform""; ""3.7. Vanishing of higher T[sup(r)][sub(i,j)]'s""; ""3.8. Harish-Chandra homomorphisms""""Chapter 4. Dual canonical bases""""4.1. Tableaux""; ""4.2. Dual canonical bases""; ""4.3. Crystals""; ""4.4. Consequences of the Kazhdan-Lusztig conjecture""; ""Chapter 5. Highest weight theory""; ""5.1. Admissible modules""; ""5.2. Gelfand-Tsetlin characters""; ""5.3. Highest weight modules""; ""5.4. Classification of admissible irreducible representations""; ""5.5. Composition multiplicities""; ""Chapter 6. Verma modules""; ""6.1. Parametrization of highest weights""; ""6.2. Characters of Verma modules""; ""6.3. The linkage principle""; ""6.4. The center of W(Ï€)""""6.5. Proof of Theorem 6.2""""Chapter 7. Standard modules""; ""7.1. Two rows""; ""7.2. Classification of finite dimensional irreducible representations""; ""7.3. Tensor products""; ""7.4. Characters of standard modules""; ""7.5. Grothendieck groups""; ""Chapter 8. Character formulae""; ""8.1. Skryabin's theorem""; ""8.2. Tensor identities""; ""8.3. Translation functors""; ""8.4. Translation commutes with duality""; ""8.5. Whittaker functor""; ""Notation""; ""Bibliography""Memoirs of the American Mathematical Society ;no. 918.Representations of quantum groupsLie superalgebrasElectronic books.Representations of quantum groups.Lie superalgebras.512/.22Brundan Jonathan1970-874462Kleshchëv A. S(Aleksandr Sergeevich),MiAaPQMiAaPQMiAaPQBOOK9910480756603321Representations of shifted Yangians and finite W-algebras1975678UNINA