Calogero-Moser systems and representation theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Zürich
European Mathematical Society
2007
|
| Series: | Zurich lectures in advanced mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references (p. [87]-89) and index |
| Physical Description: | IX, 92 S. 24 cm |
| ISBN: | 9783037190340 |
Staff View
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| 100 | 1 | |a Etingof, Pavel |d 1969- |e Verfasser |0 (DE-588)133258858 |4 aut | |
| 245 | 1 | 0 | |a Calogero-Moser systems and representation theory |c Pavel Etingof |
| 264 | 1 | |a Zürich |b European Mathematical Society |c 2007 | |
| 300 | |a IX, 92 S. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Zurich lectures in advanced mathematics | |
| 500 | |a Includes bibliographical references (p. [87]-89) and index | ||
| 650 | 4 | |a Representations of rings (Algebra) | |
| 650 | 4 | |a Associative algebras | |
| 650 | 4 | |a Representations of algebras | |
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Record in the Search Index
| _version_ | 1804137104540696576 |
|---|---|
| adam_text | Contents
Introduction
................................... 1
1
Poisson
manifolds and Hamiltonian reduction
............... 5
1.1
Poisson
manifolds
........................... 5
1.2
Moment maps
............................. 6
1.3
Hamiltonian reduction
........................ 7
1.4
Hamiltonian reduction along an orbit
................. 9
1.5
Calogero-Moser space
........................ 9
1.6
Notes
................................. 10
2
Classical mechanics and
integrable
systems
................ 11
2.1
Classical mechanics
.......................... 11
2.2
Symmetries in classical mechanics
.................. 12
2.3
Integrable
systems
.......................... 13
2.4
Action-angle variables of
integrable
systems
............. 14
2.5
Constructing
integrable
systems by Hamiltonian reduction
..... 15
2.6
The Calogero-Moser system
..................... 15
2.7
Coordinates on
f„
and the explicit form of the Calogero-Moser
system
................................. 16
2.8
The trigonometric Calogero-Moser system
............. 18
2.9
Notes
................................. 19
3
Deformation theory
............................. 21
3.1
Formal deformations of associative algebras
............. 21
3.2 Hochschild
cohomology
....................... 21
3.3 Hochschild
cohomology and deformations
.............. 23
3.4
Universal deformation
........................ 23
3.5
Quantization of
Poisson
algebras and manifolds
........... 24
3.6
Algebraic deformations
........................ 26
3.7
Notes
................................. 27
4
Moment maps, Hamiltonian reduction and the Levasseur-Stafford
theorem
................................... 29
4.1
Quantum moment maps and quantum Hamiltonian reduction
.... 29
4.2
Quantum Hamiltonian reduction
................... 30
4.3
The Levasseur-Stafford theorem
................... 30
4.4
Hamiltonian reduction with respect to an ideal in U(q)
....... 35
4.5
Quantum reduction in the deformational setting
........... 36
4.6
Notes
................................. 37
VIH
Contents
5
Quantum
mechanics,
quantum integrable
systems and the
Calogero-Moser system
.......................... 39
5.1
Quantum mechanics
.......................... 39
5.2
Quantum
integrable
systems
..................... 40
5.3
Constructing quantum
integrable
systems by quantum
Hamiltonian reduction
........................ 42
5.4
The quantum Calogero-Moser system
................ 43
5.5
Notes
................................. 44
6
Calogero-Moser systems associated to finite Coxeter groups
....... 47
6.1
Dunkl operators
............................ 47
6.2
Olshanetsky-Perelomov operators
.................. 48
6.3
Classical Dunkl operators and Olshanetsky-Perelomov
Hamiltonians
............................. 50
6.4
Notes
................................. 52
7
The rational Cherednik algebra
....................... 53
7.1
Rational Cherednik algebra and the
Poincaré-Birkhoff-Witt
theorem
53
7.2
The spherical
subalgebra
....................... 55
7.3
The localization lemma and the basic properties of Mc
....... 55
7.4
The Sl^-action on Ht<c
........................ 56
7.5
Notes
................................. 57
8
Symplectic reflection algebras
....................... 59
8.1
The definition of symplectic reflection algebras
........... 59
8.2
The PBW theorem for symplectic reflection algebras
........ 60
8.3
Koszul
algebras
............................ 60
8.4
Proof of Theorem
8.3......................... 61
8.5
The spherical
subalgebra
of the symplectic reflection algebra
.... 62
8.6
Notes
................................. 63
9
Deformation-theoretic interpretation of symplectic reflection algebras
. . 65
9.1 Hochschild
cohomology of semidirect products
........... 65
9.2
The universal deformation of
G
к
Weyl(K)
............. 67
9.3
Notes
................................. 67
10
The center of the symplectic reflection algebra
............... 69
10.1
The module
Я,,се
........................... 69
10.2
The center of
Яо,с
.......................... 70
10.3
Finite dimensional representations of
i/o,
e
.............. 70
10.4
Azumaya algebras
........................... 71
10.5
Cohen-Macaulay property and homological dimension
....... 72
10.6
Proof of Theorem
10.10........................ 74
Contents lx
10.7
The space Mc
îov G
=
Sn
...................... 75
10.8
Generalizations
............................ 77
10.9
Notes
................................. 78
11
Representation theory of rational Cherednik algebras
........... 79
11.1
Rational Cherednik algebras for any finite group of linear
transformations
............................ 79
11.2
Verma and irreducible lowest weight modules over
Яі)С
...... 79
11.3
Category
О
..............................
81
11.4
The Frobenius property
........................ 82
11.5
Representations of the rational Cherednik algebra of type A
..... 84
11.5.1
The results
........................... 84
11.5.2
Proof of Theorem
11.16.................... 85
11.6
Notes
................................. 86
Bibliography
.................................. 87
Index
......................................
91
|
| adam_txt |
Contents
Introduction
. 1
1
Poisson
manifolds and Hamiltonian reduction
. 5
1.1
Poisson
manifolds
. 5
1.2
Moment maps
. 6
1.3
Hamiltonian reduction
. 7
1.4
Hamiltonian reduction along an orbit
. 9
1.5
Calogero-Moser space
. 9
1.6
Notes
. 10
2
Classical mechanics and
integrable
systems
. 11
2.1
Classical mechanics
. 11
2.2
Symmetries in classical mechanics
. 12
2.3
Integrable
systems
. 13
2.4
Action-angle variables of
integrable
systems
. 14
2.5
Constructing
integrable
systems by Hamiltonian reduction
. 15
2.6
The Calogero-Moser system
. 15
2.7
Coordinates on
f„
and the explicit form of the Calogero-Moser
system
. 16
2.8
The trigonometric Calogero-Moser system
. 18
2.9
Notes
. 19
3
Deformation theory
. 21
3.1
Formal deformations of associative algebras
. 21
3.2 Hochschild
cohomology
. 21
3.3 Hochschild
cohomology and deformations
. 23
3.4
Universal deformation
. 23
3.5
Quantization of
Poisson
algebras and manifolds
. 24
3.6
Algebraic deformations
. 26
3.7
Notes
. 27
4
Moment maps, Hamiltonian reduction and the Levasseur-Stafford
theorem
. 29
4.1
Quantum moment maps and quantum Hamiltonian reduction
. 29
4.2
Quantum Hamiltonian reduction
. 30
4.3
The Levasseur-Stafford theorem
. 30
4.4
Hamiltonian reduction with respect to an ideal in U(q)
. 35
4.5
Quantum reduction in the deformational setting
. 36
4.6
Notes
. 37
VIH
Contents
5
Quantum
mechanics,
quantum integrable
systems and the
Calogero-Moser system
. 39
5.1
Quantum mechanics
. 39
5.2
Quantum
integrable
systems
. 40
5.3
Constructing quantum
integrable
systems by quantum
Hamiltonian reduction
. 42
5.4
The quantum Calogero-Moser system
. 43
5.5
Notes
. 44
6
Calogero-Moser systems associated to finite Coxeter groups
. 47
6.1
Dunkl operators
. 47
6.2
Olshanetsky-Perelomov operators
. 48
6.3
Classical Dunkl operators and Olshanetsky-Perelomov
Hamiltonians
. 50
6.4
Notes
. 52
7
The rational Cherednik algebra
. 53
7.1
Rational Cherednik algebra and the
Poincaré-Birkhoff-Witt
theorem
53
7.2
The spherical
subalgebra
. 55
7.3
The localization lemma and the basic properties of Mc
. 55
7.4
The Sl^-action on Ht<c
. 56
7.5
Notes
. 57
8
Symplectic reflection algebras
. 59
8.1
The definition of symplectic reflection algebras
. 59
8.2
The PBW theorem for symplectic reflection algebras
. 60
8.3
Koszul
algebras
. 60
8.4
Proof of Theorem
8.3. 61
8.5
The spherical
subalgebra
of the symplectic reflection algebra
. 62
8.6
Notes
. 63
9
Deformation-theoretic interpretation of symplectic reflection algebras
. . 65
9.1 Hochschild
cohomology of semidirect products
. 65
9.2
The universal deformation of
G
к
Weyl(K)
. 67
9.3
Notes
. 67
10
The center of the symplectic reflection algebra
. 69
10.1
The module
Я,,се
. 69
10.2
The center of
Яо,с
. 70
10.3
Finite dimensional representations of
i/o,
e
. 70
10.4
Azumaya algebras
. 71
10.5
Cohen-Macaulay property and homological dimension
. 72
10.6
Proof of Theorem
10.10. 74
Contents lx
10.7
The space Mc
îov G
=
Sn
. 75
10.8
Generalizations
. 77
10.9
Notes
. 78
11
Representation theory of rational Cherednik algebras
. 79
11.1
Rational Cherednik algebras for any finite group of linear
transformations
. 79
11.2
Verma and irreducible lowest weight modules over
Яі)С
. 79
11.3
Category
О
.
81
11.4
The Frobenius property
. 82
11.5
Representations of the rational Cherednik algebra of type A
. 84
11.5.1
The results
. 84
11.5.2
Proof of Theorem
11.16. 85
11.6
Notes
. 86
Bibliography
. 87
Index
.
91 |
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| discipline | Mathematik |
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| id | DE-604.BV022824509 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T18:41:15Z |
| indexdate | 2024-07-09T21:06:59Z |
| institution | BVB |
| isbn | 9783037190340 |
| language | English |
| lccn | 2007276038 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016029814 |
| oclc_num | 255527427 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-11 DE-83 |
| owner_facet | DE-384 DE-703 DE-11 DE-83 |
| physical | IX, 92 S. 24 cm |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | European Mathematical Society |
| record_format | marc |
| series2 | Zurich lectures in advanced mathematics |
| spelling | Etingof, Pavel 1969- Verfasser (DE-588)133258858 aut Calogero-Moser systems and representation theory Pavel Etingof Zürich European Mathematical Society 2007 IX, 92 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Zurich lectures in advanced mathematics Includes bibliographical references (p. [87]-89) and index Representations of rings (Algebra) Associative algebras Representations of algebras Hamiltonian systems Darstellungstheorie (DE-588)4148816-7 gnd rswk-swf Integrables System (DE-588)4114032-1 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 s Integrables System (DE-588)4114032-1 s Darstellungstheorie (DE-588)4148816-7 s DE-604 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016029814&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Etingof, Pavel 1969- Calogero-Moser systems and representation theory Representations of rings (Algebra) Associative algebras Representations of algebras Hamiltonian systems Darstellungstheorie (DE-588)4148816-7 gnd Integrables System (DE-588)4114032-1 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| subject_GND | (DE-588)4148816-7 (DE-588)4114032-1 (DE-588)4139943-2 |
| title | Calogero-Moser systems and representation theory |
| title_auth | Calogero-Moser systems and representation theory |
| title_exact_search | Calogero-Moser systems and representation theory |
| title_exact_search_txtP | Calogero-Moser systems and representation theory |
| title_full | Calogero-Moser systems and representation theory Pavel Etingof |
| title_fullStr | Calogero-Moser systems and representation theory Pavel Etingof |
| title_full_unstemmed | Calogero-Moser systems and representation theory Pavel Etingof |
| title_short | Calogero-Moser systems and representation theory |
| title_sort | calogero moser systems and representation theory |
| topic | Representations of rings (Algebra) Associative algebras Representations of algebras Hamiltonian systems Darstellungstheorie (DE-588)4148816-7 gnd Integrables System (DE-588)4114032-1 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| topic_facet | Representations of rings (Algebra) Associative algebras Representations of algebras Hamiltonian systems Darstellungstheorie Integrables System Hamiltonsches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016029814&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT etingofpavel calogeromosersystemsandrepresentationtheory |