000			01907nam a22002057a 4500
003			OSt
005			20240926115346.0
008			190424b ||||| |||| 00| 0 eng d
020			_a9780521436137
040			_cTata Book House _aICTS-TIFR
050			_aQA171
100			_aJames E. Humphreys
245			_aReflection groups and coxeter groups
260			_aNew York: _bCambridge University Press, _c[c1990]
300			_a204 p
490			_aCambridge Studies in Advanced Mathematics _v29
505			_aI - Finite and affine reflection groups 1 - Finite reflection groups 2 - Classification of finite reflection groups 3 - Polynomial invariants of finite reflection groups 4 - Affine reflection groups II - General theory of Coxeter groups 5 - Coxeter groups 6 - Special cases 7 - Hecke algebras and Kazhdan–Lusztig polynomials 8 - Complements
520			_aThis graduate textbook presents a concrete and up-to-date introduction to the theory of Coxeter groups. The book is self-contained, making it suitable either for courses and seminars or for self-study. The first part is devoted to establishing concrete examples. Finite reflection groups acting on Euclidean spaces are discussed, and the first part ends with the construction of the affine Weyl groups, a class of Coxeter groups that plays a major role in Lie theory. The second part (which is logically independent of, but motivated by, the first) develops from scratch the properties of Coxeter groups in general, including the Bruhat ordering and the seminal work of Kazhdan and Lusztig on representations of Hecke algebras associated with Coxeter groups is introduced. Finally a number of interesting complementary topics as well as connections with Lie theory are sketched. The book concludes with an extensive bibliography on Coxeter groups and their applications. --- summary provided by publisher
942			_2lcc _cBK
999			_c2653 _d2653