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Humphreys J.E. — Reflection groups and Coxeter groups
Humphreys J.E. — Reflection groups and Coxeter groups

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Название: Reflection groups and Coxeter groups

Автор: Humphreys J.E.

Аннотация:

In this graduate textbook Professor Humphreys presents a concrete and up-to-date introduction to the theory of Coxeter groups. He assumes that the reader has a good knowledge of algebra, but otherwise the book is self contained. The first part is devoted to establishing concrete examples; the author begins by developing the most important facts about finite reflection groups and related geometry, and showing that such groups have a Coxeter representation. In the next chapter these groups are classified by Coxeter diagrams, and actual realizations of these groups are discussed. Chapter 3 discusses the polynomial invariants of finite reflection groups, and the first part ends with a description of the affine Weyl groups and the way they arise in Lie theory. The second part (which is logically independent of, but motivated by, the first) starts by developing the properties of the Coxeter groups. Chapter 6 shows how earlier examples and others fit into the general classification of Coxeter diagrams. Chapter 7 is based on the very important work of Kazhdan and Lusztig and the last chapter presents a number of miscellaneous topics of a combinatorial nature.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1990

Количество страниц: 204

Добавлена в каталог: 10.05.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Affine group      87
Affine reflection      87
Affine Weyl group      88
Alcove      89
Alternating polynomial      69
Basic invariants      56
Bruhat ordering      118
Building      127
Cartan integer      39
Chamber      23
Class function      70
Coinvariant algebra      58
Compact hyperbolic group      140
Complex reflection group      66
Coroot      39
Coroot lattice      40
Coweight lattice      40
Coxeter complex      25 127
Coxeter element      74 174
Coxeter graph      29 31 106
Coxeter group      18 105
Coxeter number      75
Coxeter system      18 105
Crystallographic (relative to $\sigma$)      135
Crystallographic Coxeter group      137
Crystallographic group      38
Crystallographic root system      39
DEGREES      59
Deletion condition      14 117
Dihedral group      4
Dual root system      39
Dynkin diagram      39
Essential      5
Exchange condition      14 94
Exponents      75
Extended Dynkin diagram      95
Facet      25
Finite reflection group      3
Fundamental domain      22
Generic algebra      146
Geometric representation      110
Hecke algebra      150
Height of root      11
Hyperbolic Coxeter group      138
Indecomposable      35
Index of connection      40
Induced class function      70
Infinite dihedral group      88
Invariant      50
Inverse root system      39
Irreducible      30
Irreducible Coxeter system      30 129
Isotropy group      22
Jacobian criterion      63
Kazhdan — Lusztig polynomials      159
Left cell      168
Length      12 91 107
Lexicographically shellable      177
Longest element      15
Minimal coset representatives      20
Moebius function      175
Negative root      111
Negative system      8
Parabolic subgroup      19 111
Poincare polynomial      20
Poincare series      123
Positive      8
Positive definite      31
Positive root      111
Positive semidefinite      31
Positive system      8
Positive type      31
Principal minor      31
Pseudo-reflection      66
Rank      9 105
Reduced expression      12 91 108
Reflection      3 109
Reflection group      3
Reflection subgroup      172
Right cell      168
Root      6
Root lattice      40 88
Root system      6 111
Schur multiplier      181
Separates      91
Shellable      177
Simple reflections      10
Simple root      8
Simple system      8
Strong exchange condition      117
Subexpression      120
Subgraph      35
Symmetric group      5
Tits cone      126
Total ordering      7
Two-sided cell      168
Unitary reflection group      66
Universal Coxeter group      10
Upper closure      90
wall      23 90
Weak ordering      119
Weight lattice      40 88
Weyl group      39
Word problem      127
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