Affine Flag Varieties and Quantum Symmetric Pairs. (Record no. 18880)
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| fixed length control field | 06463nam a22005413i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC6229937 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240724114338.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2020 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470461386 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781470441753 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC6229937 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL6229937 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)1178755371 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA564 .F36 2020 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 516.3/53 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Fan, Zhaobing. |
| 245 10 - TITLE STATEMENT | |
| Title | Affine Flag Varieties and Quantum Symmetric Pairs. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2020. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2020. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (136 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society Series ; |
| Volume/sequential designation | v.265 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover -- Title page -- Chapter 1. Introduction -- 1.1. Background -- 1.2. The goal: affine type -- 1.3. An overview -- 1.4. The organization -- Part 1 . Affine flag varieties, Schur algebras, and Lusztig algebras -- Chapter 2. Constructions in affine type -- 2.1. Lattice presentation of affine flag varieties of type -- 2.2. Monomial basis for quantum affine _{ } -- 2.3. Algebras \bU_{ } and \bU_{ } -- Chapter 3. Lattice presentation of affine flag varieties of type -- 3.1. Affine complete flag varieties of type -- 3.2. Affine partial flag varieties of type -- 3.3. Local property at ₀ -- Chapter 4. Multiplication formulas for Chevalley generators -- 4.1. Some dimension computation -- 4.2. Standard and canonical bases of Schur algebras -- 4.3. Some multiplication formulas -- 4.4. The leading term -- Chapter 5. Coideal algebra type structures of Schur algebras and Lusztig algebras -- 5.1. The Lusztig algebra \bU_{ , }^{\fc} -- 5.2. A raw comultiplication -- 5.3. The comultiplication Δ^{\C} -- 5.4. Monomial and canonical bases of \bU^{\fc}_{ , } -- Part 2 . Lusztig algebras and coideal subalgebras of \bU(̂ _{ }) -- Chapter 6. Realization of the idempotented coideal subalgebra \bU^{\fc}_{ } of \bU(\slh_{ }) -- 6.1. The coideal subalgebra \bU^{\fc}_{ } of \bU_{ } -- 6.2. The algebra \bU^{\fc}_{ } and its monomial basis -- 6.3. Bilinear form on \bU^{\fc}_{ } -- 6.4. The canonical basis of \bU^{\fc}_{ } and positivity -- 6.5. Another presentation of the algebra \bU^{\fc}_{ } -- Chapter 7. A second coideal subalgebra of quantum affine _{\nn} -- 7.1. The Schur algebras of type \ji -- 7.2. The comultiplication -- 7.3. The monomial basis of \mbf ^{\ji}_{\nn, } -- 7.4. The coideal subalgebra of type \ji -- Chapter 8. More variants of coideal subalgebras of quantum affine _{ } -- 8.1. The Schur algebras of type \ijw. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 8.2. Comultiplication and transfer map of type \ijw -- 8.3. Quantum symmetric pair (\bU(\slh_{\nn}),\mbf ^{\ij}_{\nn}) and canonical basis on \mbf ^{\ij}_{\nn} -- 8.4. The Schur algebras of type \ii -- 8.5. Realization of a new coideal subalgebra \mbf ^{\ii}_{\mm} -- Part 3 . Schur algebras and coideal subalgebras of \bU(̂ _{ }) -- Chapter 9. The stabilization algebra \K^{\C}_{ } arising from Schur algebras -- 9.1. Monomial bases for Schur algebras -- 9.2. Stabilization of the Schur algebras -- 9.3. Comultiplication and stabilization -- 9.4. The algebra \K^{\C}_{ } and its stably canonical basis -- 9.5. The algebra \K_{ } of affine type and its comultiplication -- 9.6. The comultiplication on \K^{\C}_{ } -- 9.7. A homomorphism from \K^{\C}_{ } to \Sj -- 9.8. The algebra \K^{\C}_{ } as a subquotient of \K^{\C}_{ } -- Chapter 10. Stabilization algebras arising from other Schur algebras -- 10.1. A monomial basis for Schur algebra \Sji^{\ji}_{\nn, } -- 10.2. Stabilization of Schur algebras of type \ji -- 10.3. The stabilization algebra \K_{ }^{\ji} -- 10.4. Stabilization algebra of type \ijw -- 10.5. Stabilization algebra of type \ii -- Appendix A. Constructions in finite type -- A.1. Multiplication formulas -- A.2. Isomorphisms between type C and type B -- A.3. The comultiplication -- Nomenclature -- Bibliography -- Back Cover. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | The quantum groups of finite and affine type A admit geometric realizations in terms of partial flag varieties of finite and affine type A. Recently, the quantum group associated to partial flag varieties of finite type B/C is shown to be a coideal subalgebra of the quantum group of finite type A. In this paper the authors study the structures of Schur algebras and Lusztig algebras associated to (four variants of) partial flag varieties of affine type C. The authors show that the quantum groups arising from Lusztig algebras and Schur algebras via stabilization procedures are (idempotented) coideal subalgebras of quantum groups of affine \mathfrak{sl} and \mathfrak{gl} types, respectively. In this way, the authors provide geometric realizations of eight quantum symmetric pairs of affine types. The authors construct monomial and canonical bases of all these quantum (Schur, Lusztig, and coideal) algebras. For the idempotented coideal algebras of affine \mathfrak{sl} type, the authors establish the positivity properties of the canonical basis with respect to multiplication, comultiplication and a bilinear pairing. In particular, the authors obtain a new and geometric construction of the idempotented quantum affine \mathfrak{gl} and its canonical basis. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Flag manifolds. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Affine algebraic groups. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Quantum groups. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Schur complement. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Kazhdan-Lusztig polynomials. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Algebra, Homological. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Lai, Chun-Ju. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Li, Yiqiang. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Fan, Zhaobing |
| Title | Affine Flag Varieties and Quantum Symmetric Pairs |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2020 |
| International Standard Book Number | 9781470441753 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society Series |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=6229937">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=6229937</a> |
| Public note | Click to View |
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