Progress inMathematics Volume284 SeriesEditors HymanBass JosephOesterle´ AlanWeinstein Akihiko Gyoja Hiraku Nakajima Ken-ichi Shinoda Toshiaki Shoji Toshiyuki Tanisaki Editors Representation Theory of Algebraic Groups and Quantum Groups Editors AkihikoGyoja ToshiakiShoji NagoyaUniversity NagoyaUniversity GraduateSchoolofMathematics GraduateSchoolofMathematics Chikusa-ku Chikusa-ku Nagoya,464-8602 Nagoya,464-8602 Japan Japan [email protected] [email protected] HirakuNakajima ToshiyukiTanisaki KyotoUniversity OsakaCityUniversity ResearchInstitute GraduateSchoolofScience forMathematicalSciences Sumiyoshi-ku Kyoto,606-8502 Osaka,558-8585 Japan Japan [email protected] [email protected] Ken-ichiShinoda SophiaUniversity FacultyofScienceandTechnology DepartmentofInformation andCommunicationSciences Chiyoda-ku Tokyo,102-8554 Japan [email protected] ISBN978-0-8176-4696-7 e-ISBN978-0-8176-4697-4 DOI10.1007/978-0-8176-4697-4 SpringerNewYorkDordrechtHeidelbergLondon MathematicsSubjectClassification(2010):17B37,16Gxx,17B67,20C08,17B20,17B35,20G15, 22E65,14M15,14L30 (cid:2)c SpringerScience+BusinessMedia,LLC2010 Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewritten permissionofthepublisher (Springer ScienceCBusiness Media, LLC,233Spring Street, New York, NY10013, USA),except forbrief excerpts inconnection with reviews orscholarly analysis. Usein connectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware, orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden. Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyare notidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubject toproprietaryrights. Printedonacid-freepaper www.birkhauser-science.com Contents Preface............................................................................... ix Program............................................................................. xi QuotientCategoriesofModularRepresentations.............................. 1 HenningHaahrAndersen Dipper–James–Murphy’sConjecturefor Hecke Algebras ofTypeBn........................................................................... 17 SusumuArikiandNicolasJacon OnDominoInsertionandKazhdan–LusztigCellsinTypeBn ............... 33 Ce´dricBonnafe´,MeinolfGeck,LacrimioaraIancu, andThomasLam RunnerRemovalMoritaEquivalences .......................................... 55 JosephChuangandHyoheMiyachi Appendix: ModuleCorrespondencesinRouquierBlocksofFiniteGeneral LinearGroups...................................................................... 81 AkihikoHidaandHyoheMiyachi Quantum gl , q-Schur Algebras and Their n Infinite/InfinitesimalCounterparts............................................... 93 JieDuandQiangFu CherednikAlgebrasforAlgebraicCurves......................................121 MichaelFinkelbergandVictorGinzburg ATemperley–LiebAnaloguefortheBMWAlgebra...........................155 G.I.LehrerandR.B.Zhang vii viii Contents GradedLieAlgebrasandIntersectionCohomology...........................191 G.Lusztig CrystalBaseElementsofanExtremalWeightModuleFixed byaDiagramAutomorphismII:CaseofAffineLieAlgebras ................225 SatoshiNaitoandDaisukeSagaki t-Analogsof q-Charactersof Quantum Affine Algebras ofTypeE6,E7,E8..................................................................257 HirakuNakajima Ultra-Discretization of the G.1/-Geometric Crystals 2 totheD.3/-PerfectCrystals.......................................................273 4 ToshikiNakashima OnHeckeAlgebrasAssociatedwithEllipticRootSystems ...................297 YoshihisaSaitoandMidoriShiota Green’s Formula with C(cid:3)-Action and Caldero–Keller’s FormulaforClusterAlgebras ....................................................313 JieXiaoandFanXu