000			04992nam a22004813i 4500
001			EBC4908273
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005			20240729131328.0
006			m o d |
007			cr cnu||||||||
008			240724s2017 xx o ||||0 eng d
020			_a9781470436032 _q(electronic bk.)
020			_z9781470422493
035			_a(MiAaPQ)EBC4908273
035			_a(Au-PeEL)EBL4908273
035			_a(CaPaEBR)ebr11409819
035			_a(OCoLC)965547796
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA564.K547 2017
082	0		_a512.48199999999997
100	1		_aKleshchev, Alexander.
245	1	0	_aImaginary Schur-Weyl Duality.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2017.
264		4	_c©2016.
300			_a1 online resource (108 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society ; _vv.245
505	0		_aCover -- Title page -- Chapter 1. Introduction -- 1.1. Convex preorders and cuspidal systems -- 1.2. Imaginary representations -- 1.3. Imaginary Schur-Weyl duality -- 1.4. Imaginary Howe and Ringel dualities -- 1.5. Gelfand-Graev words and representations -- 1.6. Example: type ₁⁽¹⁾ -- 1.7. Structure of the paper -- 1.8. Acknowledgements -- Chapter 2. Preliminaries -- 2.1. Partitions and compositions -- 2.2. Coset representatives -- 2.3. Schur algebras -- 2.4. Representation theory of Schur algebras -- 2.5. Induction and restriction for Schur algebras -- 2.6. Schur functors -- Chapter 3. Khovanov-Lauda-Rouquier algebras -- 3.1. Lie theoretic notation -- 3.2. The definition and first properties -- 3.3. Basic representation theory of _{\al} -- 3.4. Induction, coinduction, and duality for KLR algebras -- 3.5. Crystal operators and extremal words -- 3.6. Mackey Theorem -- 3.7. Convex preorders and root partitions -- 3.8. Cuspidal systems and standard modules -- 3.9. Colored imaginary tensor spaces -- Chapter 4. Imaginary Schur-Weyl duality -- 4.1. Imaginary tensor space and its parabolic analogue -- 4.2. Action of \Si_{ } on _{ } -- 4.3. Imaginary Schur algebras -- 4.4. Characteristic zero theory -- 4.5. Imaginary induction and restriction -- Chapter 5. Imaginary Howe duality -- 5.1. Gelfand-Graev modules -- 5.2. Imaginary symmetric, divided, and exterior powers -- 5.3. Parabolic analogues -- 5.4. Schur algebras as endomorphism algebras -- 5.5. Projective generator for imaginary Schur algebra -- Chapter 6. Morita equaivalence -- 6.1. Morita equivalence functors -- 6.2. Induction and Morita equivalence -- 6.3. Alternative definitions of standard modules -- 6.4. Base change -- 6.5. Ringel duality and double centralizer properties -- Chapter 7. On formal characters of imaginary modules -- 7.1. Weight multiplicities in \La^{\la^{\tr}}( _{ℎ}).
505	8		_a7.2. Gelfand-Graev words and shuffles -- 7.3. Gelfand-Graev fragment of the formal character of \Dede(\la) -- 7.4. Imaginary Jacobi-Trudy formula -- Chapter 8. Imaginary tensor space for non-simply-laced types -- 8.1. Minuscule representations for non-simply-laced types -- 8.2. The endomorphism ᵣ: _{ }→ _{ } for non-simply-laced types -- Bibliography -- Back Cover.
520			_aThe authors study imaginary representations of the Khovanov-Lauda-Rouquier algebras of affine Lie type. Irreducible modules for such algebras arise as simple heads of standard modules. In order to define standard modules one needs to have a cuspidal system for a fixed convex preorder. A cuspidal system consists of irreducible cuspidal modules-one for each real positive root for the corresponding affine root system {\tt X}_l^{(1)}, as well as irreducible imaginary modules-one for each l-multiplication. The authors study imaginary modules by means of "imaginary Schur-Weyl duality" and introduce an imaginary analogue of tensor space and the imaginary Schur algebra. They construct a projective generator for the imaginary Schur algebra, which yields a Morita equivalence between the imaginary and the classical Schur algebra, and construct imaginary analogues of Gelfand-Graev representations, Ringel duality and the Jacobi-Trudy formula.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic 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	_aDuality theory (Mathematics).
655		4	_aElectronic books.
700	1		_aMuth, Robert.
776	0	8	_iPrint version: _aKleshchev, Alexander _tImaginary Schur-Weyl Duality _dProvidence : American Mathematical Society,c2017 _z9781470422493
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4908273 _zClick to View
999			_c128017 _d128017