Lectures on the Orbit Method

430 Pages·2004·28.29 MB·English

by  A. A. Kirillov

Lectures on the
Orbit Method

A.A. Kirillov
Lectures on the
Orbit Method

Lectures on the
Orbit Method

AA. Kirillov

Graduate Studies
in Mathernaties
Volume 64

‘American Mathematial Society
Providence, Rhode Itand
EDITORIAL COMMITTEE

Walter Croig
Nikola ancy
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Contents

Pretce
Tntroduetion

‘Chapter 1. Geometry of Coadjoimt Orbite
$1. Basie defitions
1L1. Gondjoin: representation
12. Canonical form aq
1D, Syomplcte steuctise un emadjoint exits
2.1 The fit (original appro,
2.2, The seound (Puison) approach
124, The tied (aympleti reduction} approsch
2.4. Iabegaty vodltlon
{4 Coodjnn: invartnt funtions
23. General properties of invavants
2, Benmplas
{$4 The moment ap
‘41. The universal property of conjoint orbite
42, Some particule aoe
$8. Polasizstions
5.1. Elements of symplectic geometry

532, Tnwraak poatiationt on hemgensows eytpletfe man-

tds
vi coments

‘Chapter 2. Raptesentations and Orbita of the Heisenberg Group 3
$1. Heisenberg Lis algebra and Heicenborg Lie group 32
11. Souve realizations 2
1.2, Universal enveloping agora Up) 35
1.8. The Heisenberg Lie algebra asa contraction a
$2. Conunicel cotwnutation teletons 39
2, Creatiom aod unaitation operators 39
2.2, Twosided ideals in 0(5) a
23. H. Weyl velomalation of CCR a
244, ‘The standacd relation of CCR 8
2. Other realizations of CCR 6
26, Unlgueneat than, ®
58, Represeatation theory for the Heseoberg xroup a

31, The unitary dual a
3.2, The generalized characters of HE ra
2.3. The infinitesimal chargeves of 1 eo
34, The tear product of unirrepe 0
{H, Coadjoint orbite ofthe Heisenberg group a
4.1, Description of eaedjint exh 6
42, Spmplestic forms on orbits und the Poison structure
ay e
4.3, Projections of eoudoim orbits #8
5. Orbits aud ecpresentations %
5.1, Restriction induction princpla and eanteustion of
vunirepe
52. Other rules ofthe User's Guide
98, Polerzations
6.1. Real polarizations
62. Ceanpler polarnitions
63. Divorce polarizations

Chapter 3, The Orbit Method for Nupotent Lie Groupe n
EL. Generales 08 ailpotet ie yom cm

$2. Comaments on the User's Guide n

2A. The unitary dual .
Gomenes

2.2, ‘The construction of wnirepe
2.3, Restriction induction functors
2.4. Generslved charantere
26, [ninitsimal eharactere
246. Functional dimension
27, Plancherd meseore
$8, Workout ample
3. The unary dunt
142. Construction of unireps
3, Restriction functor
3.4 Indetion functor
85. Decompasition of « tawor product of two woirtpes
‘36, Generalized chararters
£7. Enfalesimal eharacers
128, Ponctional dimension
3.9. Plancherel measure
8.10, Other examples
$4. Proofs
4.1. Nilpotent groupe with 2edlenensonal center
42, The main indvction procsdune
413. ‘The image of Eg) sad the Fanetional dimension
44. The exgvence of generals characters
45, Homeomorphism of G and O(@)

Clapter 4. Sohable Lie Groups

81, Exponential Lie groups
111, Generates
112, Puluraaiy condition
13, Resteetiondudvetion functors
14, Gonershzod charactere
13. InBsiesiosl characters
82, Genet aable Lie gp
2.1, Teme and wld Lie groupe
22, Taau vbvable Lie gure

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