A double Hall algebra approach to affine quantum Schur-Weyl theory:
The theory of Schur–Weyl duality has had a profound influence over many areas of algebra and combinatorics. This text is original in two respects: it discusses affine q-Schur algebras and presents an algebraic, as opposed to geometric, approach to affine quantum Schur–Weyl theory. To begin, various...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2012
|
| Series: | London Mathematical Society lecture note series
401 |
| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| Summary: | The theory of Schur–Weyl duality has had a profound influence over many areas of algebra and combinatorics. This text is original in two respects: it discusses affine q-Schur algebras and presents an algebraic, as opposed to geometric, approach to affine quantum Schur–Weyl theory. To begin, various algebraic structures are discussed, including double Ringel–Hall algebras of cyclic quivers and their quantum loop algebra interpretation. The rest of the book investigates the affine quantum Schur–Weyl duality on three levels. This includes the affine quantum Schur–Weyl reciprocity, the bridging role of affine q-Schur algebras between representations of the quantum loop algebras and those of the corresponding affine Hecke algebras, presentation of affine quantum Schur algebras and the realisation conjecture for the double Ringel–Hall algebra with a proof of the classical case. This text is ideal for researchers in algebra and graduate students who want to master Ringel–Hall algebras and Schur–Weyl duality |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (viii, 207 pages) |
| ISBN: | 9781139226660 |
| DOI: | 10.1017/CBO9781139226660 |
Staff View
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| 520 | |a The theory of Schur–Weyl duality has had a profound influence over many areas of algebra and combinatorics. This text is original in two respects: it discusses affine q-Schur algebras and presents an algebraic, as opposed to geometric, approach to affine quantum Schur–Weyl theory. To begin, various algebraic structures are discussed, including double Ringel–Hall algebras of cyclic quivers and their quantum loop algebra interpretation. The rest of the book investigates the affine quantum Schur–Weyl duality on three levels. This includes the affine quantum Schur–Weyl reciprocity, the bridging role of affine q-Schur algebras between representations of the quantum loop algebras and those of the corresponding affine Hecke algebras, presentation of affine quantum Schur algebras and the realisation conjecture for the double Ringel–Hall algebra with a proof of the classical case. This text is ideal for researchers in algebra and graduate students who want to master Ringel–Hall algebras and Schur–Weyl duality | ||
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Record in the Search Index
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| any_adam_object | |
| author | Deng, Bangming |
| author_facet | Deng, Bangming |
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| author_sort | Deng, Bangming |
| author_variant | b d bd |
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| contents | Introduction -- Preliminaries -- Double Ringel-Hall algebras of cyclic quivers -- Affine quantum Schur algebras and the Schur-Weyl reciprocity -- Representations of affine quantum Schur algebras -- The presentation and realization problems -- The classical (v=1) case |
| ctrlnum | (ZDB-20-CBO)CR9781139226660 (OCoLC)847040716 (DE-599)BVBBV043941948 |
| dewey-full | 515.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV043941948 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9781139226660 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350918 |
| oclc_num | 847040716 |
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| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (viii, 207 pages) |
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| publishDate | 2012 |
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| publisher | Cambridge University Press |
| record_format | marc |
| series2 | London Mathematical Society lecture note series |
| spelling | Deng, Bangming Verfasser aut A double Hall algebra approach to affine quantum Schur-Weyl theory Bangming Deng, Jie Du, Qiang Fu Cambridge Cambridge University Press 2012 1 online resource (viii, 207 pages) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 401 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Introduction -- Preliminaries -- Double Ringel-Hall algebras of cyclic quivers -- Affine quantum Schur algebras and the Schur-Weyl reciprocity -- Representations of affine quantum Schur algebras -- The presentation and realization problems -- The classical (v=1) case The theory of Schur–Weyl duality has had a profound influence over many areas of algebra and combinatorics. This text is original in two respects: it discusses affine q-Schur algebras and presents an algebraic, as opposed to geometric, approach to affine quantum Schur–Weyl theory. To begin, various algebraic structures are discussed, including double Ringel–Hall algebras of cyclic quivers and their quantum loop algebra interpretation. The rest of the book investigates the affine quantum Schur–Weyl duality on three levels. This includes the affine quantum Schur–Weyl reciprocity, the bridging role of affine q-Schur algebras between representations of the quantum loop algebras and those of the corresponding affine Hecke algebras, presentation of affine quantum Schur algebras and the realisation conjecture for the double Ringel–Hall algebra with a proof of the classical case. This text is ideal for researchers in algebra and graduate students who want to master Ringel–Hall algebras and Schur–Weyl duality Schur functions Weyl groups Representations of Lie groups Affine algebraic groups Quantengruppe (DE-588)4252437-4 gnd rswk-swf Schur-Algebra (DE-588)4180242-1 gnd rswk-swf Weyl-Gruppe (DE-588)4065886-7 gnd rswk-swf Schur-Algebra (DE-588)4180242-1 s Weyl-Gruppe (DE-588)4065886-7 s Quantengruppe (DE-588)4252437-4 s 1\p DE-604 Du, Jie Sonstige oth Fu, Qiang Sonstige oth Erscheint auch als Druckausgabe 978-1-107-60860-3 https://doi.org/10.1017/CBO9781139226660 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Deng, Bangming A double Hall algebra approach to affine quantum Schur-Weyl theory Introduction -- Preliminaries -- Double Ringel-Hall algebras of cyclic quivers -- Affine quantum Schur algebras and the Schur-Weyl reciprocity -- Representations of affine quantum Schur algebras -- The presentation and realization problems -- The classical (v=1) case Schur functions Weyl groups Representations of Lie groups Affine algebraic groups Quantengruppe (DE-588)4252437-4 gnd Schur-Algebra (DE-588)4180242-1 gnd Weyl-Gruppe (DE-588)4065886-7 gnd |
| subject_GND | (DE-588)4252437-4 (DE-588)4180242-1 (DE-588)4065886-7 |
| title | A double Hall algebra approach to affine quantum Schur-Weyl theory |
| title_auth | A double Hall algebra approach to affine quantum Schur-Weyl theory |
| title_exact_search | A double Hall algebra approach to affine quantum Schur-Weyl theory |
| title_full | A double Hall algebra approach to affine quantum Schur-Weyl theory Bangming Deng, Jie Du, Qiang Fu |
| title_fullStr | A double Hall algebra approach to affine quantum Schur-Weyl theory Bangming Deng, Jie Du, Qiang Fu |
| title_full_unstemmed | A double Hall algebra approach to affine quantum Schur-Weyl theory Bangming Deng, Jie Du, Qiang Fu |
| title_short | A double Hall algebra approach to affine quantum Schur-Weyl theory |
| title_sort | a double hall algebra approach to affine quantum schur weyl theory |
| topic | Schur functions Weyl groups Representations of Lie groups Affine algebraic groups Quantengruppe (DE-588)4252437-4 gnd Schur-Algebra (DE-588)4180242-1 gnd Weyl-Gruppe (DE-588)4065886-7 gnd |
| topic_facet | Schur functions Weyl groups Representations of Lie groups Affine algebraic groups Quantengruppe Schur-Algebra Weyl-Gruppe |
| url | https://doi.org/10.1017/CBO9781139226660 |
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