000			04611nam a22005053i 4500
001			EBC3114298
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005			20240729124605.0
006			m o d |
007			cr cnu||||||||
008			240724s2015 xx o ||||0 eng d
020			_a9781470420314 _q(electronic bk.)
020			_z9781470409609
035			_a(MiAaPQ)EBC3114298
035			_a(Au-PeEL)EBL3114298
035			_a(CaPaEBR)ebr11040302
035			_a(OCoLC)922982042
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA247 -- .H577 2014eb
082	0		_a512/.482
100	1		_aHiss, Gerhard.
245	1	0	_aImprimitive Irreducible Modules for Finite Quasisimple Groups.
250			_a1st ed.
264		1	_aProvidence, RI : _bAmerican Mathematical Society, _c2015.
264		4	_c©2014.
300			_a1 online resource (126 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society ; _vv.234
505	0		_aCover -- Title page -- Acknowledgements -- Chapter 1. Introduction -- Chapter 2. Generalities -- 2.1. Comments on the notation -- 2.2. Conditions for primitivity -- 2.3. Some results on linear groups of small degree -- 2.4. Reduction modulo ℓ and imprimitivity -- 2.5. A result on polynomials -- Chapter 3. Sporadic Groups and the Tits Group -- Chapter 4. Alternating Groups -- Chapter 5. Exceptional Schur Multipliers and Exceptional Isomorphisms -- 5.1. Description of the tables -- 5.2. The proofs -- Chapter 6. Groups of Lie type: Induction from non-parabolic subgroups -- 6.1. Outline of the strategy -- 6.2. The classical groups of Lie type -- 6.3. The exceptional groups of Lie type -- Chapter 7. Groups of Lie type: Induction from parabolic subgroups -- 7.1. Harish-Chandra series -- 7.2. Lusztig series -- 7.3. Asymptotics -- Chapter 8. Groups of Lie type: char( )=0 -- 8.1. Some results on Weyl groups -- 8.2. Harish-Chandra series -- 8.3. Lusztig series -- Chapter 9. Classical groups: ℎ ( )=0 -- 9.1. The groups -- 9.2. Harish-Chandra series -- 9.3. Lusztig series -- 9.4. Examples for the restriction to commutator subgroups -- Chapter 10. Exceptional groups -- 10.1. The exceptional groups of type and -- 10.2. Explicit results on some exceptional groups -- Bibliography -- Back Cover.
520			_aMotivated by the maximal subgroup problem of the finite classical groups the authors begin the classification of imprimitive irreducible modules of finite quasisimple groups over algebraically closed fields K. A module of a group G over K is imprimitive, if it is induced from a module of a proper subgroup of G. The authors obtain their strongest results when {\rm char}(K) = 0, although much of their analysis carries over into positive characteristic. If G is a finite quasisimple group of Lie type, they prove that an imprimitive irreducible KG-module is Harish-Chandra induced. This being true for \mbox{\rm char}(K) different from the defining characteristic of G, the authors specialize to the case {\rm char}(K) = 0 and apply Harish-Chandra philosophy to classify irreducible Harish-Chandra induced modules in terms of Harish-Chandra series, as well as in terms of Lusztig series. The authors determine the asymptotic proportion of the irreducible imprimitive KG-modules, when G runs through a series groups of fixed (twisted) Lie type. One of the surprising outcomes of their investigations is the fact that these proportions tend to 1, if the Lie rank of the groups tends to infinity. For exceptional groups G of Lie type of small rank, and for sporadic groups G, the authors determine all irreducible imprimitive KG-modules for arbitrary characteristic of K.
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	_aAlgebraic fields.
650		0	_aFinite groups.
650		0	_aSemisimple Lie groups.
655		4	_aElectronic books.
700	1		_aHusen, William J.
700	1		_aMagaard, Kay.
776	0	8	_iPrint version: _aHiss, Gerhard _tImprimitive Irreducible Modules for Finite Quasisimple Groups _dProvidence, RI : American Mathematical Society,c2015 _z9781470409609
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114298 _zClick to View
999			_c69817 _d69817