LEADER 03352nam 2200481 450 001 996418450303316 005 20210211130958.0 010 $a981-15-7387-5 024 7 $a10.1007/978-981-15-7387-3 035 $a(CKB)4100000011457783 035 $a(DE-He213)978-981-15-7387-3 035 $a(MiAaPQ)EBC6350800 035 $a(PPN)250219077 035 $a(EXLCZ)994100000011457783 100 $a20210211d2020 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aElliptic quantum groups $erepresentations and related geometry /$fHitoshi Konno 205 $a1st ed. 2020. 210 1$aSingapore :$cSpringer,$d[2020] 210 4$dİ2020 215 $a1 online resource (XIII, 131 p. 3 illus.) 225 1 $aSpringerBriefs in Mathematical Physics ;$vVolume 37 311 $a981-15-7386-7 327 $aPreface -- Acknowledgements -- Chapter 1: Introduction -- Chapter 2: Elliptic Quantum Group -- Chapter 3: The H-Hopf Algebroid Structure of -- Chapter 4: Representations of -- Chapter 5: The Vertex Operators -- Chapter 6: Elliptic Weight Functions -- Chapter 7: Tensor Product Representation -- Chapter 8: Elliptic q-KZ Equation -- Chapter 9: Related Geometry -- Appendix A -- Appendix B -- Appendix C -- Appendix D -- Appendix E -- References. 330 $aThis is the first book on elliptic quantum groups, i.e., quantum groups associated to elliptic solutions of the Yang-Baxter equation. Based on research by the author and his collaborators, the book presents a comprehensive survey on the subject including a brief history of formulations and applications, a detailed formulation of the elliptic quantum group in the Drinfeld realization, explicit construction of both finite and infinite-dimensional representations, and a construction of the vertex operators as intertwining operators of these representations. The vertex operators are important objects in representation theory of quantum groups. In this book, they are used to derive the elliptic q-KZ equations and their elliptic hypergeometric integral solutions. In particular, the so-called elliptic weight functions appear in such solutions. The author?s recent study showed that these elliptic weight functions are identified with Okounkov?s elliptic stable envelopes for certain equivariant elliptic cohomology and play an important role to construct geometric representations of elliptic quantum groups. Okounkov?s geometric approach to quantum integrable systems is a rapidly growing topic in mathematical physics related to the Bethe ansatz, the Alday-Gaiotto-Tachikawa correspondence between 4D SUSY gauge theories and the CFT?s, and the Nekrasov-Shatashvili correspondences between quantum integrable systems and quantum cohomology. To invite the reader to such topics is one of the aims of this book. 410 0$aSpringerBriefs in mathematical physics ;$vVolume 37. 606 $aQuantum groups 606 $aElliptic functions 615 0$aQuantum groups. 615 0$aElliptic functions. 676 $a512.55 700 $aKonno$b Hitoshi$0993675 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418450303316 996 $aElliptic quantum groups$92275318 997 $aUNISA