ENGLISH

Quantum groups and quantum cohomology

By Davesh Maulik; Andrei Okounkov

Book information

Year
2019
ISBN
9782856299005, 2856299008
Language
english
Format
PDF
Filesize
3 MB (3564850 bytes)
Series
Astérisque
Pages
\225
Time added
2022-05-20 21:44:48

Description

Chapter 1. Introduction 1.1. Fundamental structures and conjectures 1.2. Baxter subalgebras and quantum multiplication 1.3. Quantum multiplication by divisors 1.4. Shift operators and qKZ 1.5. Yangian of gl(1)"0362gl(1) and instanton moduli 1.6. Further directions 1.7. Update 1.8. Acknowledgments Part I. General Theory Chapter 2. Nakajima varieties 2.1. Definition 2.2. Basic properties 2.3. Torus-fixed points 2.4. Tensor product of Nakajima varieties 2.5. Slices 2.6. Minuscule coweights Chapter 3. Stable envelopes 3.1. Assumptions and conventions 3.2. Basic constructions 3.3. Characterization of stable envelopes 3.4. Lagrangian residues 3.5. Proof of existence 3.6. Torus restriction 3.7. Symplectic resolutions Chapter 4. Properties of R-matrices 4.1. Definition and braid relations 4.2. Changing the torus 4.3. Covers and factorization of R-matrices 4.4. Adjoint operators 4.5. Unitarity 4.6. Action of Steinberg correspondences 4.7. Vacuum matrix elements 4.8. Classical R-matrices 4.9. Diagonal matrix elements of R-matrices 4.10. Flops and stable envelopes Chapter 5. Yangians 5.1. Tensor products 5.2. Construction of Yangians 5.3. The Lie algebra gQ 5.4. Operators of classical multiplication 5.5. The structure of the Yangian Chapter 6. Further properties of the Yangian 6.1. The core Yangian 6.2. Slices and intertwiners 6.3. The dual Yangian 6.4. Intertwiners and relations 6.5. Baxter subalgebras and Casimir connection Chapter 7. Quantum multiplication 7.1. Preliminaries 7.2. Modified reduced operators 7.3. Broken curves 7.4. Proof of Theorem 7.2.1 7.5. Additivity Chapter 8. Shift operators 8.1. Definition 8.2. Intertwining property 8.3. Shift operators are quantum operators Chapter 9. Minuscule shifts and R-matrices 9.1. Setup 9.2. Properness 9.3. Computation of S() Chapter 10. Quantum multiplication by divisors 10.1. Classical multiplication by divisors 10.2. Quantum operators Chapter 11. Cotangent bundles of Grassmannians 11.1. Quantum cohomology 11.2. The stable basis 11.3. Yangian action Part II. Instanton moduli Chapter 12. Classical r-matrix and gl(1)"0362gl(1). 12.1. Setup 12.2. Baranovsky operators 12.3. Proof of Theorem 12.2.1 12.4. Classical r-matrix Chapter 13. Free bosons 13.1. Fock spaces 13.2. Insertions and coproducts 13.3. Virasoro algebra 13.4. Reflection operator Chapter 14. The full R-matrix 14.1. Zero modes 14.2. Cup product by divisor 14.3. R-matrix as a Virasoro intertwiner 14.4. The 1/u expansion of R Chapter 15. Quantum multiplication for M(r,n) 15.1. Explicit formulas 15.2. Generation statement Chapter 16. Gamma functions 16.1. The bundle V"0362V 16.2. Barnes' -function 16.3. The matrix R"0362R Chapter 17. Core Yangian modulo 17.1. Semiclassical R-matrix 17.2. Stable basis for `39`42`"613A``45`47`"603AHilbn 17.3. Differential operators on C and gl() 17.4. Plücker relations Chapter 18. The Yangian of gl(1)"0362gl(1) 18.1. Generators of the core Yangian 18.2. Slices and screening operators Chapter 19. Yangian and vertex algebras 19.1. The operator Q"055BQcl 19.2. Yangian and W-algebras Bibliography

Similar books

Session C11: Ancient Cultural Landscapes in South Europe – their Ecological Setting and Evolution, Session C22: Gardeners from South America, Session S04: Agro-Pastoralism and Early Metallurgy Sessions, Session WS29: The Idea of Enclosure in Recent Iberian Prehistory, Session C88: Rhytmes et causalites des dynamiques de l'anthropisation en Europe entre 6500 ET 500 BC: Hypotheses socio-culturelles et/ou climatiques: Proceedings of the XV UISPP World Congress (Lisbon 4-9 September 2006) / Actes du XV Congrès Mondial (Lisbonne 4-9 Septembre 2006) Vol.36

Session C11: Ancient Cultural Landscapes in South Europe – their Ecological Setting and Evolution, Session C22: Gardeners from South America, Session S04: Agro-Pastoralism and Early Metallurgy Sessions, Session WS29: The Idea of Enclosure in Recent Iberian Prehistory, Session C88: Rhytmes et causalites des dynamiques de l'anthropisation en Europe entre 6500 ET 500 BC: Hypotheses socio-culturelles et/ou climatiques: Proceedings of the XV UISPP World Congress (Lisbon 4-9 September 2006) / Actes du XV Congrès Mondial (Lisbonne 4-9 Septembre 2006) Vol.36

2010 · PDF

THE BRITISH ARMY IN INDIA: ITS PRESERVATION BY AN APPROPRIATE CLOTHING, HOUSING, LOCATING, RECREATIVE EMPLOYMENT, AND HOPEFUL ENCOURAGEMENT OF THE TROOPS. with AN APPENDIX ON INDIA : THE CLIMATE OP ITS HILLS ; THE DEVELOPMENT OF ITS RESODRCBS, INDUSTRY, AND ARTS ; THE ADMINISTRATION OF JUSTICE ; THE BLACK ACT ; THE PROGRESS OF CHRISTIANITY ; THE TRAFFIC IN OPIUM ; THE VALUE OF INDIA ; PERMANENT CAUSES OF DISAFFECTION, AND OF THE RECENT REBELLION ; THE TRADITIONARY POLICY; MISGOVERNMENT BY NATIVE RULERS ; ANNEXATIONS OF THEIR TERRITORY, ETC.

THE BRITISH ARMY IN INDIA: ITS PRESERVATION BY AN APPROPRIATE CLOTHING, HOUSING, LOCATING, RECREATIVE EMPLOYMENT, AND HOPEFUL ENCOURAGEMENT OF THE TROOPS. with AN APPENDIX ON INDIA : THE CLIMATE OP ITS HILLS ; THE DEVELOPMENT OF ITS RESODRCBS, INDUSTRY, AND ARTS ; THE ADMINISTRATION OF JUSTICE ; THE BLACK ACT ; THE PROGRESS OF CHRISTIANITY ; THE TRAFFIC IN OPIUM ; THE VALUE OF INDIA ; PERMANENT CAUSES OF DISAFFECTION, AND OF THE RECENT REBELLION ; THE TRADITIONARY POLICY; MISGOVERNMENT BY NATIVE RULERS ; ANNEXATIONS OF THEIR TERRITORY, ETC.

1858 · PDF

Idries Shah 27 Books Collection : A Perfumed Scorpion, A Veiled Gazelle, Caravan of Dreams, Darkest England, Destination Mecca, Evenings with Idries Shah, Knowing How to Know, Learning How to Learn, Letters and Lectures of Idries Shah, Neglected aspects of Sufi study, Observations, Oriental Magic, Reflections, Seeker after Truth, Special Illumination, Special Problems in the study of Sufi ideas, Sufi thought and action, Tales of the Dervishes, The Dermis Probe, The Elephant in the Dark, The Englishman Handbook, Idries Shah Antology, The Magic Monastery, The natives are restless, wisdom of the Idiots PDF.

Idries Shah 27 Books Collection : A Perfumed Scorpion, A Veiled Gazelle, Caravan of Dreams, Darkest England, Destination Mecca, Evenings with Idries Shah, Knowing How to Know, Learning How to Learn, Letters and Lectures of Idries Shah, Neglected aspects of Sufi study, Observations, Oriental Magic, Reflections, Seeker after Truth, Special Illumination, Special Problems in the study of Sufi ideas, Sufi thought and action, Tales of the Dervishes, The Dermis Probe, The Elephant in the Dark, The Englishman Handbook, Idries Shah Antology, The Magic Monastery, The natives are restless, wisdom of the Idiots PDF.

2022 · PDF

The travels of Capts. Lewis and Clarke from St. Louis, by way of the Missouri and Columbia rivers, to the Pacific ocean; performed in the years 1804, 1805 & 1806, by order of the government of the United States. Containing delineations of the manners, customs, religion, &c. of the Indians, comp. from various authentic sources, and original documents, and a summary of the Statistical view of the Indian nations, from the official communication of Meriwether Lewis. Illustrated with a map of the country, inhabited by the western tribes of Indians

The travels of Capts. Lewis and Clarke from St. Louis, by way of the Missouri and Columbia rivers, to the Pacific ocean; performed in the years 1804, 1805 & 1806, by order of the government of the United States. Containing delineations of the manners, customs, religion, &c. of the Indians, comp. from various authentic sources, and original documents, and a summary of the Statistical view of the Indian nations, from the official communication of Meriwether Lewis. Illustrated with a map of the country, inhabited by the western tribes of Indians

1809 · PDF

Professional Linux kernel architecture ''Wrox programmer to programmer''--Cover. - ''What you are reading right now is the result of an evolution over more than seven years: After two years of writing, the first edition was published in German by Carl Hanser Verlag in 2003. It then described kernel 2.6.0. The test was used as a basis for the low-level design documentation for the EAL4+ security evaluation of Red Hat Enterprise Linux 5, requiring to update it to kernel 2.6.18 (if the EAL acronym does not mean anything to you, then Wikipedia is once more your friend). Hewlett-Packard sponsored the translation into English and has, thankfully, granted the rights to publish the result. Updates to kernel 2.6.24 were then performed specifically for this book''--P. ix

Professional Linux kernel architecture ''Wrox programmer to programmer''--Cover. - ''What you are reading right now is the result of an evolution over more than seven years: After two years of writing, the first edition was published in German by Carl Hanser Verlag in 2003. It then described kernel 2.6.0. The test was used as a basis for the low-level design documentation for the EAL4+ security evaluation of Red Hat Enterprise Linux 5, requiring to update it to kernel 2.6.18 (if the EAL acronym does not mean anything to you, then Wikipedia is once more your friend). Hewlett-Packard sponsored the translation into English and has, thankfully, granted the rights to publish the result. Updates to kernel 2.6.24 were then performed specifically for this book''--P. ix

2008 · PDF