000 03284nam a22005055i 4500
001 978-3-642-11175-4
003 DE-He213
005 20190213151258.0
007 cr nn 008mamaa
008 100301s2010 gw | s |||| 0|eng d
020 _a9783642111754
_9978-3-642-11175-4
024 7 _a10.1007/978-3-642-11175-4
_2doi
050 4 _aQA174-183
072 7 _aPBG
_2bicssc
072 7 _aMAT002010
_2bisacsh
072 7 _aPBG
_2thema
082 0 4 _a512.2
_223
100 1 _aBroué, Michel.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aIntroduction to Complex Reflection Groups and Their Braid Groups
_h[electronic resource] /
_cby Michel Broué.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2010.
300 _aXII, 144 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1988
505 0 _aPreliminaries -- Prerequisites and Complements in Commutative Algebra -- Polynomial Invariants of Finite Linear Groups -- Finite Reflection Groups in Characteristic Zero -- Eigenspaces and Regular Elements.
520 _aWeyl groups are particular cases of complex reflection groups, i.e. finite subgroups of GLr(C) generated by (pseudo)reflections. These are groups whose polynomial ring of invariants is a polynomial algebra. It has recently been discovered that complex reflection groups play a key role in the theory of finite reductive groups, giving rise as they do to braid groups and generalized Hecke algebras which govern the representation theory of finite reductive groups. It is now also broadly agreed upon that many of the known properties of Weyl groups can be generalized to complex reflection groups. The purpose of this work is to present a fairly extensive treatment of many basic properties of complex reflection groups (characterization, Steinberg theorem, Gutkin-Opdam matrices, Solomon theorem and applications, etc.) including the basic findings of Springer theory on eigenspaces. In doing so, we also introduce basic definitions and properties of the associated braid groups, as well as a quick introduction to Bessis' lifting of Springer theory to braid groups.
650 0 _aGroup theory.
650 0 _aAlgebra.
650 0 _aAlgebraic topology.
650 1 4 _aGroup Theory and Generalizations.
_0http://scigraph.springernature.com/things/product-market-codes/M11078
650 2 4 _aCommutative Rings and Algebras.
_0http://scigraph.springernature.com/things/product-market-codes/M11043
650 2 4 _aAssociative Rings and Algebras.
_0http://scigraph.springernature.com/things/product-market-codes/M11027
650 2 4 _aAlgebraic Topology.
_0http://scigraph.springernature.com/things/product-market-codes/M28019
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642111846
776 0 8 _iPrinted edition:
_z9783642111747
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1988
856 4 0 _uhttps://doi.org/10.1007/978-3-642-11175-4
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c10131
_d10131