Cabanes M., Enguehard M., Bollobas B. (Ed) — Representation Theory of Finite Reductive Groups (New Mathematical Monographs Series), Vol. 1 :: Электронная библиотека попечительского совета мехмата МГУ

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Cabanes M., Enguehard M., Bollobas B. (Ed) — Representation Theory of Finite Reductive Groups (New Mathematical Monographs Series), Vol. 1

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Название: Representation Theory of Finite Reductive Groups (New Mathematical Monographs Series), Vol. 1

Авторы: Cabanes M., Enguehard M., Bollobas B. (Ed)

Аннотация:

At the crossroads of representation theory, algebraic geometry and finite group theory, this book blends together many of the main concerns of modern algebra, synthesising the past 25 years of research, with full proofs of some of the most remarkable achievements in the area. Cabanes and Enguehard follow three main themes: first, applications of étale cohomology, leading to the proof of the recent Bonnafé-Rouquier theorems. The second is a straightforward and simplified account of the Dipper-James theorems relating irreducible characters and modular representations. The final theme is local representation theory. One of the main results here is the authors' version of Fong-Srinivasan theorems. Throughout the text is illustrated by many examples and background is provided by several introductory chapters on basic results and appendices on algebraic geometry and derived categories. The result is an essential introduction for graduate students and reference for all algebraists.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 2004

Количество страниц: 436

Добавлена в каталог: 27.05.2008

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Предметный указатель

l-modular, xvii $\cap\downarrow$ -stable      6
Lan, the Lang map      103
Lang’s map, theorem      104
Levi decomposition, Levi subgroup      394
Lie algebra of G      393
Local structure, information      360
Locally closed subvariety      391
Lusztig      xii
Mapping cone      375
Max(A), affine variety associated with A      389
Morphism of varieties or schemes of finite type      398
Morphism of varieties or schemes, compactifiable      408
Morphism of varieties or schemes, dominant      396
Morphism of varieties or schemes, etale      404
Morphism of varieties or schemes, finite      395
Morphism of varieties or schemes, flat      404
Morphism of varieties or schemes, proper      399
Morphism of varieties or schemes, quasi-finite      395
Morphism of varieties or schemes, separable      396
Morphism of varieties or schemes, separated      398
Normalization      396
Null homotopic      376
O(w)      397
Open-closed exact sequence      411
Order on simplicial scheme      58
Order, Bruhat      397
Order, lexicographic      292
Order, local      172
Order, polynomial      119
Partition of an integer, $\lambda\vdash n$       78
Perfect complex      381
Perfect isometry      139
Point, closed, generic, geometric      398
Polynomial order      190
Presheaf      382
Primes, bad      193
Primes, good      193
Principal block      77
Proj      386
Projection formula      412
Puig’s conjecture      370
Purity (cohomological)      413
Purity of branch locus      396
Quasi-affinity criterion      401
Quasi-isomorphism      57 376
Ramification      417 418
Regular linear character of U      301
Regular variety      392
RF, right derived functor      379
RHom      381
Root datum, root system      119 394
Scheme      397
Sh(X),       383
Sheaf      383
Sheaf over X      399
Sheaf, ample (coherent)      400
Sheaf, coherent      400
Sheaf, constant      383 406
Sheaf, constructible      406
Sheaf, dual      406
Sheaf, etale      405
Sheaf, generated by its local sections      400
Sheaf, locally constant      384 406
Sheaf, tensor product of      385
Sheaf, torsion      405
Sheaf, very ample      400
Sheafification, $\mathcal{F} \mapsto \mathcal{F}^+$       383 405
Simplex, simplicial scheme      57
Size of a partition      78

Smooth      392
soc(M)      xvi
Spec(A)      397
Split Levi subgroup (E-)      190
Splitting system      xvi
Stalk      382 405 411
Standard tableaux      279
Steinberg module      95 301
Strict henselization, $A^{sh}$       411
Subgroup, $\phi_E-$       190
Subgroup, Borel      394
Subgroup, Levi      394
Subgroup, parabolic      28
Subpair, inclusion      76
Subpair, maximal      76
Subpair, self-centralizing      352
Subpair, “connected”      334
Subquotient      3
Subscript notation with variable symbols, $G_{\pi}$ , $\pi$ -elements of a group G      xv
Subscript notation with variable symbols, , constant sheaf on X with stalk M      383
Subscript notation with variable symbols, $T_{\phi_E}$ , (T a torus, E a set of integers), maximal $\phi_E$ -subgroup of T      191
Subscript notation with variable symbols, $\mathcal{F}_x$ , stalk at a point      382
Subscript notation with variable symbols, $\mathcal{F}_{\bar{x}}$ , stalk at a geometric point      405
Symmetric algebra      12
S[v, w]      164
T, a torus      394
Tangent map, tangent sheaf      392
Tensor product of sheaves      399 406
Tits system      27
Torus      394
Triangle (distinguished)      378
Triangulated category      382
Triangulation      58
Twin characters      216
Twisted induction      125
Twisted inverse image       413
TYPE      121
T[v, w]      164
Uniform function      126 133
Unipotent block      135
Unipotent irreducible character      127
Unipotent radical      394
Variety, (quasi-)projective      391
Variety, affine      389
Variety, complete      391
Variety, defined over $\mathbb{F}_q$       395
Variety, Deligne — Lusztig      110
Variety, G-quotient      396
Variety, interval      166
Variety, irreducible      391
Variety, normal      396
Variety, quasi-affine      391
Variety, regular      392
Variety, Schubert      397
Variety, smooth      392
Vector bundle      401
vinvertible (coherent)      400
X(w), subvariety of G/B      111 146
X[v, w]      166
Y(w), with $w \in W$ , subvariety of G/U      111 146
Young diagrams, tableaux      279
Y[v, w]      166
Z(H), center of the group H      xv
Zariski — Nagata      396
Zariski, topology      390
Zariski’s main theorem      396
[a, b], a commutator      xv
|G : H|, index of H in G      xv
|X|, cardinality of the set X      xv

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