000			02721nam a22004098i 4500
001			CR9781139226660
003			UkCbUP
005			20200124160236.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			120109s2012||||enk o ||1 0|eng|d
020			_a9781139226660 (ebook)
020			_z9781107608603 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050		4	_aQA331.7 _b.D46 2012
082	0	4	_a515.9 _223
100	1		_aDeng, Bangming, _eauthor.
245	1	2	_aA double Hall algebra approach to affine quantum Schur-Weyl theory / _cBangming Deng, Jie Du, Qiang Fu.
264		1	_aCambridge : _bCambridge University Press, _c2012.
300			_a1 online resource (viii, 207 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aLondon Mathematical Society lecture note series ; _v401
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_aIntroduction -- 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.
520			_aThe 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.
650		0	_aSchur functions.
650		0	_aWeyl groups.
650		0	_aRepresentations of Lie groups.
650		0	_aAffine algebraic groups.
700	1		_aDu, Jie, _eauthor.
700	1		_aFu, Qiang, _eauthor.
776	0	8	_iPrint version: _z9781107608603
830		0	_aLondon Mathematical Society lecture note series ; _v401.
856	4	0	_uhttps://doi.org/10.1017/CBO9781139226660
999			_c518127 _d518125