半单群的表示论(第1卷)

所属分类:数学  
出版时间:2011-1   出版时间:世界图书出版公司   作者:Anthony W. Knapp   页数:384  
Tag标签:数学,代数  

内容概要

本书是一部经典的著作,分为上下两卷,前十章为上卷,后六章为下卷。书中讲述半单李群表示理论的方式给出了本科目的精华,符合学习的自然规律。定理陈述地相当详细,增加了许多经典的解释性例子。本章末都有习题,对于学习研究生和科研工作者相当有用。目次:理论概述;su(2),su(2,r)和su(2,c)表示论;c∞向量和通用包络代数;紧李群表示论;非紧群的理论;全纯离散系列;导出表示论;可允许表示论;离散系列的结构;全局性质;plancherel公式;不可约表示论;最小k型;酉表示;附录:李群的基本理论;偏微分方程的常规奇异点;经典群的根和受限根。

书籍目录

preface
to
the
princeton
landmarks
in
mathematics
edition
preface
acknowledgments
chapter
i.
scope
of
the
theory
1.the
classical
groups
2.cartan
decomposition
3.representations
4.concrete
problems
in
representation
theory
5.
abstract
theory
for
compact
groups
6.application
of
the
abstract
theory
to
lie
groups
7.problems
chapter
ii.
representations
of
su(2),
sl(2,
r),
and
sl(2,
c)
1.the
unitary
trick
2.irreducible
finite-dimensional
complex-linear
representations
of
si(2,
c)
3.finite-dimensional
representations
of
s1(2,
c)
4.irreducible
unitary
representations
of
sl(2,
c)
5.irreducible
unitary
representations
of
sl(2,
r)
6.use
of
su(1,
1)
7.plancherel
formula
8.problems
chapter
iii.
c∞
vectors
and
the
universal
enveloping
algebra
1.universal
enveloping
algebra
2.actions
on
universal
enveloping
algebra
3.c∞vectors
4.gatrding
subspace
5.problems
chapter
iv.
representations
of
compact
lie
groups
1.examples
of
root
space
decompositions
2.roots
3.abstract
root
systems
and
positivity
4.weyl
group,
algebraically
5.weights
and
integral
forms
6.centalizers
of
tori
7.theorem
of
the
highest
weight
8.verma
modules
9.weyl
group,
analytically
10.weyl
character
formula
11.problems
chapter
v.
structure
theory
for
noncompact
groups
1.cartan
decomposition
and
the
unitary
trick
2.iwasawa
decomposition
3.regular
elements,
weyl
chambers,
and
the
weyl
group
4.other
decompositions
5.parabolic
subgroups
6.integral
formulas
7.borel-weil
theorem
8.problems
chapter
vi.
holomorphic
discrete
series
1.holomorphic
discrete
series
for
su(1,
1)
2.classical
bounded
symmetric
domains
3.harish-chandra
decomposition
4.holomorphic
discrete
series
5.finiteness
of
an
integral
6.problems
chapter
vii.
induced
representations
1.three
pictures
2.elementary
properties
3.bruhat
theory
4.formal
intertwining
operators
5.gindikin-karpelevi
formula
6.estimates
on
intertwining
operators,
part
i
7.analytic
continuation
of
intertwining
operators,
part
i
8.spherical
functions
9.finite-dimensional
representations
and
the
h
function
10.estimates
on
intertwining
operators,
part
ii
11.tempered
representations
and
langlands
quotients
12.problems
chapter
viii.
admissible
representations
1.motivation
2.admissible
representations
3.invariant
subspaces
4.framework
for
studying
matrix
coefficients
5.harish-chandra
homomorphism
6.infinitesimal
character
7.differential
equations
satisfied
by
matrix
coefficients
8.asymptotic
expansions
and
leading
exponents
9.first
application:
subrepresentation
theorem
10.second
application:
analytic
continuation
of
interwining
operators,
part
ii
11.third
application:
control
of
k-finite
z(gc)-finite
functions
12.asymptotic
expansions
near
the
walls
13.fourth
application:
asymptotic
size
of
matrix
coefficients
14.fifth
application:
identification
of
irreducible
tempered
representations
15.sixth
application:
langlands
classification
of
irreducible
admissible
representations
16.problems
chapter
ix.
construction
of
discrete
series
1.infinitesimally
unitary
representations
2.a
third
way
of
treating
admissible
representations
3.equivalent
definitions
of
discrete
series
4.motivation
in
general
and
the
construction
in
su(1,
1)
5.finite-dimensional
spherical
representations
6.duality
in
the
general
case
7.construction
of
discrete
series
8.limitations
on
k
types
9.lemma
on
linear
independence
10.problems
chapter
x.
global
characters
1.existence
2.character
formulas
for
sl(2,
r)
3.induced
characters
4.differential
equations
5.analyticity
on
the
regular
set,
overview
and
example
6.analyticity
on
the
regular
set,
general
case
7.formula
on
the
regular
set
8.behavior
on
the
singular
set
9.families
of
admissible
representations
10.problems
chapter
xi.
introduction
to
plancherel
formula
1.constructive
proof
for
su(2)
2.constructive
proof
for
sl(2,
c)
3.constructive
proof
for
sl(2,
r)
4.ingredients
of
proof
for
general
case
5.scheme
of
proof
for
general
case
6.properties
of
fi
7.hirai's
patching
conditions
8.problems
chapter
xii.
exhaustion
of
discrete
series
1.boundedness
of
numerators
of
characters
2.use
of
patching
conditions
3.formula
for
discrete
series
characters
4.schwartz
space
5.exhaustion
of
discrete
series
6.tempered
distributions
7.limits
of
discrete
series
8.discrete
series
of
m
9.schrnid's
identity
10.problems
chapter
xiii.
plancherel
formula
1.ideas
and
ingredients
2.real-rank-one
groups,
part
i
3.real-rank-one
groups,
part
ii
4.averaged
discrete
series
5.sp
(2,
r)
6.general
case
7.problems
chapter
xiv.
irreducible
tempered
representations
1.sl(2,
r)
from
a
more
general
point
of
view
2.eisenstein
integrals
3.asymptotics
of
eisenstein
integrals
4.the
η
functions
for
intertwining
operators
5.first
irreducibility
results
6.normalization
of
intertwining
operators
and
reducibility
7.connection
with
plancherel
formula
when
dim
a
=
1
8.harish-chandra's
completeness
theorem
9.r
group
10.action
by
weyl
group
on
representations
of
m
11.multiplicity
one
theorem
12.zuckerman
tensoring
of
induced
representations
13.generalized
schmid
identities
14.inversion
of
generalized
schmid
identities
15.complete
reduction
of
induced
representations
16.classification
17.revised
langlands
classification
18.problems
chapter
my.
minimal
k
types
1.definition
and
formula
2.inversion
problem
3.connection
with
intertwining
operators
4.problems
chapter
xvi.
unitary
representations
1.sl(2,
r)
and
sl(2,
c)
2.continuity
arguments
and
complementary
series
3.criterion
for
unitary
representations
4.reduction
to
real
infinitesimal
character
5.problems
appendix
a:
elementary
theory
of
lie
groups
1.lie
algebras
2.structure
theory
of
lie
algebras
3.fundamental
group
and
covering
spaces
4.topological
groups
5.vector
fields
and
submanifolds
6.lie
groups
appendix
b:
regular
singular
points
of
partial
differential
equations
1.summary
of
classical
one-variable
theory
2.uniqueness
and
analytic
continuation
of
solutions
in
several
variables
3.analog
of
fundamental
matrix
4.regular
singularities
5.systems
of
higher
order
6.leading
exponents
and
the
analog
of
the
indicial
equation
7.uniqueness
of
representation
appendix
c:
roots
and
restricted
roots
for
classical
groups
1.complex
groups
2.noncompact
real
groups
3.roots
vs.
restricted
roots
in
noncompact
real
groups
notes
references
index
of
notation
index

图书封面

图书标签Tags

数学,代数


    半单群的表示论(第1卷)下载



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