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Lang S. — SL2: With 33 Figures
Lang S. — SL2: With 33 Figures

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Название: SL2: With 33 Figures

Автор: Lang S.

Аннотация:

SL2(R) gives the student an introduction to the infinite dimensional representation theory of semisimple Lie groups by concentrating on one example - SL2(R). This field is of interest not only for its own sake, but for its connections with other areas such as number theory, as brought out, for example, in the work of Langlands. The rapid development of representation theory over the past 40 years has made it increasingly difficult for a student to enter the field. This book makes the theory accessible to a wide audience, its only prerequisites being a knowledge of real analysis, and some differential equations.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 428

Добавлена в каталог: 30.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
${C}^{\infty}$ vector      93
${L}^{2}$-kernel      12
${S}_{m,n}$      19
Absolute value of operator      159
Adjoint of operator      369
Adjoint representation      102 105 137
Admissible      26 105
Analytic map      98
Analytic vector      99 198
Analyticity      411
Asymptotic expansion      83
Basic estimate      401
Bi-invariant      51
Bounded operator      355
Bounded representation      1
Bruhat decomposition      210 252
Cartan decomposition      139
Casimir operator      194
Centralizers      193
CHARACTER      19 46
Closed operator      370
Coefficient functions      29 47
Compact groups      26
Compact operator      10 232 383
Complementary series      123
Complete reducibility      234
Completely reducible      10
Contained (operators)      370
Coset spaces      37
Cusp      222
Cusp form      228
Cuspidal      219
Cuspidal part of resolvent      295 299
Dense subspace      8
Derived representation      94
Dirac sequence      5
Discrete series      107 120 179
Distributions      394 409
Eigenf unctions of Casimir      199
Eigenf unctions of Laplacian      314
Eisenstein, formalism      310
Eisenstein, functions      33
Eisenstein, operator      339
Eisenstein, series      244
Eisenstein, transform      346
Elliptic operators      389
Embedding      9
EQUIVALENCE      9
Essentially self-adjoint      372
Fixed vector      25
Fundamental domain      223
G-isomorphism      106
Generate topologically      61
Generators and relations      209
Green's functions      287
H(s)      46
Harish transform on A      49 69 148 153
Harish transform on K      154 166
Highest weight vector      104
Hilbert — Schmidt operator      127
Induced representation      44
Infinitesimal isomorphism      106
Integral formulas      67 134
Intertwining operators      9
Invariant measure      37
Invariant subspace      8
Irreducible      9
Isomorphism      9
Iwasawa decomposition      39
Jordan space      383
K-bi-invariant      51
K-finite      25
Laplacian      270
Lie algebra      89
Lie derivative      90
Lifting of weight m      187
Lowest weight vector      104
Mellin transform      49 74 248
Meromorphic family of operators      38
Mock discrete series      120
Morphism      9
Multiplicity      10
Occur      9
One parameter subgroup      90
Orthogonal decomposition      10
Paley — Wiener space      75
Partial isometry      156
Plancherel formula      16 82 173
Polar decomposition      155
Polynomial growth      227
Positive definite function      62
Principal series      47
Projections      363
Rapidly decreasing      249
Regular element      132
Regular map      27
Regularity theorem      404 407
Representation      1
Resolvent formula      379
Resolvent of Laplace operator      275
Resolving form      273
Schur's lemma      362
Self-adjoint      370
Siegel set      235
Spectral family      365
Spectral measure      378
Spectral theorem for bounded operator      360
Spectral theorem for compact operator      10
Spectral theorem for unbounded operator      378
Spherical function      47 55 199
Spherical transform      78
Star closed      12 54
Strictly admissible      26 129
Strongly continuous      1
Symmetric operator      370
Symmetry of Laplace operator      280
Theta transform      240
Topological generator      61
Trace      14 124 128
Trace class      128 158
Trace in discrete series      150
Trace in induced representation      49 147
Type of function      244
type of operator      297
Unimodular      2
Unipotent      219
Unitarization      108
Unitary      1
Unitary character      46
Universal enveloping algebra      192
Upper half-plane      41
Weak analyticity      411 415
Weak topology      1
Weil representation      211
Weyl element      69
Weyl group      69
Whittaker equation      290
Zeta transform      243
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