04084nam 22007695 450 99646650290331620200705132903.01-280-39164-297866135695613-642-11175-010.1007/978-3-642-11175-4(CKB)2670000000007035(SSID)ssj0000449727(PQKBManifestationID)11924047(PQKBTitleCode)TC0000449727(PQKBWorkID)10449657(PQKB)10334841(DE-He213)978-3-642-11175-4(MiAaPQ)EBC3065023(PPN)14907865X(EXLCZ)99267000000000703520100301d2010 u| 0engurnn|008mamaatxtccrIntroduction to Complex Reflection Groups and Their Braid Groups[electronic resource] /by Michel Broué1st ed. 2010.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2010.1 online resource (XII, 144 p.) Lecture Notes in Mathematics,0075-8434 ;1988Bibliographic Level Mode of Issuance: Monograph3-642-11174-2 3-642-11184-X Includes bibliographical references and index.Preliminaries -- Prerequisites and Complements in Commutative Algebra -- Polynomial Invariants of Finite Linear Groups -- Finite Reflection Groups in Characteristic Zero -- Eigenspaces and Regular Elements.Weyl 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.Lecture Notes in Mathematics,0075-8434 ;1988Group theoryCommutative algebraCommutative ringsAssociative ringsRings (Algebra)Algebraic topologyGroup Theory and Generalizationshttps://scigraph.springernature.com/ontologies/product-market-codes/M11078Commutative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11043Associative Rings and Algebrashttps://scigraph.springernature.com/ontologies/product-market-codes/M11027Algebraic Topologyhttps://scigraph.springernature.com/ontologies/product-market-codes/M28019Group theory.Commutative algebra.Commutative rings.Associative rings.Rings (Algebra).Algebraic topology.Group Theory and Generalizations.Commutative Rings and Algebras.Associative Rings and Algebras.Algebraic Topology.512.2MAT 203fstubSI 850rvkBroué Michelauthttp://id.loc.gov/vocabulary/relators/aut478936BOOK996466502903316Introduction to complex reflection groups and their braid groups261779UNISA