國立虎尾科技大學 |

Elliptic Quantum Groups = Representations and Related Geometry /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Elliptic Quantum Groups/ by Hitoshi Konno.
Reminder of title:	Representations and Related Geometry /
Author:	Konno, Hitoshi.
Description:	XIII, 131 p. 3 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Mathematical physics. -
Online resource:	https://doi.org/10.1007/978-981-15-7387-3
ISBN:	9789811573873

Elliptic Quantum Groups = Representations and Related Geometry /
Konno, Hitoshi.

Elliptic Quantum GroupsRepresentations and Related Geometry /[electronic resource] :by Hitoshi Konno. - 1st ed. 2020. - XIII, 131 p. 3 illus.online resource. - SpringerBriefs in Physics,372197-1757 ;. - SpringerBriefs in Physics,.

Preface -- 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.

This 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.

ISBN: 9789811573873

Standard No.: 10.1007/978-981-15-7387-3doiSubjects--Topical Terms:

527831
Mathematical physics.

LC Class. No.: QA401-425

Dewey Class. No.: 530.15

Elliptic Quantum Groups = Representations and Related Geometry /
LDR:03337nam a22004095i 4500 001 1029179
003 DE-He213
005 20210316202441.0
007 cr nn 008mamaa
008 210318s2020 si | s |||| 0|eng d
020 $a 9789811573873 $9 978-981-15-7387-3
024 7 $a 10.1007/978-981-15-7387-3 $2 doi
035 $a 978-981-15-7387-3
050 4 $a QA401-425
050 4 $a QC19.2-20.85
072 7 $a PHU $2 bicssc
072 7 $a SCI040000 $2 bisacsh
072 7 $a PHU $2 thema
082 0 4 $a 530.15 $2 23
100 1 $a Konno, Hitoshi. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1325802
245 1 0 $a Elliptic Quantum Groups $h [electronic resource] : $b Representations and Related Geometry / $c by Hitoshi Konno.
250 $a 1st ed. 2020.
264 1 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2020.
300 $a XIII, 131 p. 3 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a SpringerBriefs in Physics, $x 2197-1757 ; $v 37
505 0 $a Preface -- 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.
520 $a This 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.
650 0 $a Mathematical physics. $3 527831
650 0 $a Group theory. $3 527791
650 0 $a Algebra. $2 gtt $3 579870
650 0 $a Ordered algebraic structures. $3 672366
650 1 4 $a Mathematical Physics. $3 786661
650 2 4 $a Group Theory and Generalizations. $3 672112
650 2 4 $a Order, Lattices, Ordered Algebraic Structures. $3 670104
650 2 4 $a Mathematical Applications in the Physical Sciences. $3 786649
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9789811573866
776 0 8 $i Printed edition: $z 9789811573880
830 0 $a SpringerBriefs in Physics, $x 2191-5423 $3 1253586
856 4 0 $u https://doi.org/10.1007/978-981-15-7387-3
912 $a ZDB-2-PHA
912 $a ZDB-2-SXP
950 $a Physics and Astronomy (SpringerNature-11651)
950 $a Physics and Astronomy (R0) (SpringerNature-43715)