Representation theory and geometry of the flag variety:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Boston
De Gruyter
[2023]
|
| Schriftenreihe: | De Gruyter Studies in Mathematics
Volume 90 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | VIII, 125 Seiten Diagramme |
| ISBN: | 9783110766905 3110766906 |
Internformat
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| 100 | 1 | |a McGovern, William M. |d 1959- |e Verfasser |0 (DE-588)124769179 |4 aut | |
| 245 | 1 | 0 | |a Representation theory and geometry of the flag variety |c William M. McGovern |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2023] | |
| 264 | 4 | |c © 2023 | |
| 300 | |a VIII, 125 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter Studies in Mathematics |v Volume 90 | |
| 650 | 4 | |a Darstellungstheorie | |
| 650 | 4 | |a Geometrie | |
| 650 | 4 | |a Vektorräume | |
| 650 | 4 | |a lineare Transformationen | |
| 650 | 7 | |a MATHEMATICS / Algebra / General |2 bisacsh | |
| 653 | |a Darstellungstheorie | ||
| 653 | |a lineare Transformationen | ||
| 653 | |a Vektorräume | ||
| 653 | |a Geometrie | ||
| 653 | |a Darstellungstheorie; lineare Transformationen; Vektorräume; Geometrie | ||
| 653 | |a Polynomial representations; orbital varieties; Kazhdan–Lusztig polynomials; Hecke algebra; Lusztig–Vogan polynomials; pattern avoidance | ||
| 710 | 2 | |a Walter de Gruyter GmbH & Co. KG |0 (DE-588)10095502-2 |4 pbl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, PDF |z 978-3-11-076694-3 |
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| 830 | 0 | |a De Gruyter Studies in Mathematics |v Volume 90 |w (DE-604)BV000005407 |9 90 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-034006289 | ||
Datensatz im Suchindex
| _version_ | 1804184763754348544 |
|---|---|
| adam_text | CONTENTS
PREFACE
-
V
1
1.1
1.2
1.3
1.4
1.5
1.6
PRELIMINARIES
-
1
STRUCTURE
OF
G
-
1
THE
FLAG
VARIETY
-
1
FINITE-DIMENSIONAL
AND
HIGHEST
WEIGHT
REPRESENTATIONS
-
2
SYMMETRIC
SUBGROUPS
OF
G
----
4
HARISH-CHANDRA
MODULES
AND
DIFFERENTIAL
OPERATORS
ON
G/B
-
5
NILPOTENT
ORBITS
AND
ORBITAL
VARIETIES
-
7
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
POLYNOMIAL
REPRESENTATIONS
AND
THE
FLAG
VARIETY
-
10
SCHUR
MODULES
-
10
IDENTIFICATION
AND
IRREDUCIBILITY
OF
THE
MODULES
VH
-
14
DEFINING
EQUATIONS
OF
THE
FLAG
VARIETY
----
16
COHOMOLOGY
OF
THE
FLAG
VARIETY
-
19
SYMPLECTIC
GROUPS
-
24
ORTHOGONAL
GROUPS
----
24
THE
GENERAL
CASE
AND
LINE
BUNDLES
-----26
3
3.1
3.2
3.3
3.4
ASSOCIATED,
CHARACTERISTIC,
AND
ORBITAL
VARIETIES
-
27
DEFINITIONS
OF
THE
CHARACTERISTIC
VARIETY
AND
MOMENT
MAP
----
27
K-ORBITS
IN
X
----
29
THE
CLOSURE
ORDER
ON
K-ORBITS
-
33
ORBITAL
VARIETIES
AND
SPRINGER
FIBERS
-
37
4
4.1
4.2
4.3
SINGULARITIES
OF
ORBIT
CLOSURES
-
46
SMOOTH
AND
RATIONALLY
SMOOTH
POINTS
-
46
CRITERION
FOR
RATIONAL
SMOOTHNESS
-
47
SYMMETRIC
VARIETIES
-
50
5
5.1
5.2
5.3
5.4
5.5
5.6
5.7
KAZHDAN-LUSZTIG
POLYNOMIALS
AND
THE
HECKE
ALGEBRA
----
53
THE
HECKE
ALGEBRA
AND
THE
^-POLYNOMIALS
-
53
KAZHDAN-LUSZTIG
POLYNOMIALS
-
55
ANOTHER
CONSTRUCTION
----
58
INVERSE
KL
POLYNOMIALS
-
60
CONES,
CELLS,
AND
W-GRAPHS
-
61
APPLICATIONS
TO
REPRESENTATION
THEORY
-
65
APPLICATIONS
TO
GEOMETRY
----
72
BIBLIOGRAPHY
-
115
VIII
-
CONTENTS
6
6.1
6.2
6.3
6.4
LUSZTIG-VOGAN
POLYNOMIALS
AND
HARISH-CHANDRA
MODULES
-
77
Z/2Z
DATA
----
77
CIRCLE
AND
CROSS
ACTIONS
-
80
THE
HECKE
MODULE
----
82
APPLICATIONS
----
85
7
7.1
7.2
7.3
7.4
7.5
PATTERN
AVOIDANCE
AND
SINGULARITIES
OF
ORBIT
CLOSURES
-
88
PATTERN
AVOIDANCE
FOR
CLASSICAL
SCHUBERT
VARIETIES
-
88
ROOT
SUBSYSTEM
PATTERN
AVOIDANCE
----
90
PATTERN
AVOIDANCE
FOR
SYMMETRIC
VARIETIES
-
94
RICHARDSON
VARIETIES
AND
SYMMETRIC
ORBITS
IN
TYPE
AIII
-
99
INTERVAL
PATTERN
AVOIDANCE
-
101
8
8.1
8.2
8.3
8.4
SPRINGER
FIBERS
-
105
THE
TWO-COLUMN
CASE
----
105
PARTICULAR
COMPONENTS
----
107
COHOMOLOGY
OF
SPRINGER
FIBERS
----
110
ORBITAL
VARIETIES
IN
GENERAL
----
111
INDEX
-
123
|
| adam_txt |
CONTENTS
PREFACE
-
V
1
1.1
1.2
1.3
1.4
1.5
1.6
PRELIMINARIES
-
1
STRUCTURE
OF
G
-
1
THE
FLAG
VARIETY
-
1
FINITE-DIMENSIONAL
AND
HIGHEST
WEIGHT
REPRESENTATIONS
-
2
SYMMETRIC
SUBGROUPS
OF
G
----
4
HARISH-CHANDRA
MODULES
AND
DIFFERENTIAL
OPERATORS
ON
G/B
-
5
NILPOTENT
ORBITS
AND
ORBITAL
VARIETIES
-
7
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
POLYNOMIAL
REPRESENTATIONS
AND
THE
FLAG
VARIETY
-
10
SCHUR
MODULES
-
10
IDENTIFICATION
AND
IRREDUCIBILITY
OF
THE
MODULES
VH
-
14
DEFINING
EQUATIONS
OF
THE
FLAG
VARIETY
----
16
COHOMOLOGY
OF
THE
FLAG
VARIETY
-
19
SYMPLECTIC
GROUPS
-
24
ORTHOGONAL
GROUPS
----
24
THE
GENERAL
CASE
AND
LINE
BUNDLES
-----26
3
3.1
3.2
3.3
3.4
ASSOCIATED,
CHARACTERISTIC,
AND
ORBITAL
VARIETIES
-
27
DEFINITIONS
OF
THE
CHARACTERISTIC
VARIETY
AND
MOMENT
MAP
----
27
K-ORBITS
IN
X
----
29
THE
CLOSURE
ORDER
ON
K-ORBITS
-
33
ORBITAL
VARIETIES
AND
SPRINGER
FIBERS
-
37
4
4.1
4.2
4.3
SINGULARITIES
OF
ORBIT
CLOSURES
-
46
SMOOTH
AND
RATIONALLY
SMOOTH
POINTS
-
46
CRITERION
FOR
RATIONAL
SMOOTHNESS
-
47
SYMMETRIC
VARIETIES
-
50
5
5.1
5.2
5.3
5.4
5.5
5.6
5.7
KAZHDAN-LUSZTIG
POLYNOMIALS
AND
THE
HECKE
ALGEBRA
----
53
THE
HECKE
ALGEBRA
AND
THE
^-POLYNOMIALS
-
53
KAZHDAN-LUSZTIG
POLYNOMIALS
-
55
ANOTHER
CONSTRUCTION
----
58
INVERSE
KL
POLYNOMIALS
-
60
CONES,
CELLS,
AND
W-GRAPHS
-
61
APPLICATIONS
TO
REPRESENTATION
THEORY
-
65
APPLICATIONS
TO
GEOMETRY
----
72
BIBLIOGRAPHY
-
115
VIII
-
CONTENTS
6
6.1
6.2
6.3
6.4
LUSZTIG-VOGAN
POLYNOMIALS
AND
HARISH-CHANDRA
MODULES
-
77
Z/2Z
DATA
----
77
CIRCLE
AND
CROSS
ACTIONS
-
80
THE
HECKE
MODULE
----
82
APPLICATIONS
----
85
7
7.1
7.2
7.3
7.4
7.5
PATTERN
AVOIDANCE
AND
SINGULARITIES
OF
ORBIT
CLOSURES
-
88
PATTERN
AVOIDANCE
FOR
CLASSICAL
SCHUBERT
VARIETIES
-
88
ROOT
SUBSYSTEM
PATTERN
AVOIDANCE
----
90
PATTERN
AVOIDANCE
FOR
SYMMETRIC
VARIETIES
-
94
RICHARDSON
VARIETIES
AND
SYMMETRIC
ORBITS
IN
TYPE
AIII
-
99
INTERVAL
PATTERN
AVOIDANCE
-
101
8
8.1
8.2
8.3
8.4
SPRINGER
FIBERS
-
105
THE
TWO-COLUMN
CASE
----
105
PARTICULAR
COMPONENTS
----
107
COHOMOLOGY
OF
SPRINGER
FIBERS
----
110
ORBITAL
VARIETIES
IN
GENERAL
----
111
INDEX
-
123 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | McGovern, William M. 1959- |
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| bvnumber | BV048631268 |
| classification_rvk | SK 240 |
| ctrlnum | (OCoLC)1350790869 (DE-599)BVBBV048631268 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV048631268 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T21:16:03Z |
| indexdate | 2024-07-10T09:44:31Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110766905 3110766906 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034006289 |
| oclc_num | 1350790869 |
| open_access_boolean | |
| owner | DE-11 DE-29T |
| owner_facet | DE-11 DE-29T |
| physical | VIII, 125 Seiten Diagramme |
| publishDate | 2023 |
| publishDateSearch | 2023 |
| publishDateSort | 2023 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter Studies in Mathematics |
| series2 | De Gruyter Studies in Mathematics |
| spelling | McGovern, William M. 1959- Verfasser (DE-588)124769179 aut Representation theory and geometry of the flag variety William M. McGovern Berlin ; Boston De Gruyter [2023] © 2023 VIII, 125 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier De Gruyter Studies in Mathematics Volume 90 Darstellungstheorie Geometrie Vektorräume lineare Transformationen MATHEMATICS / Algebra / General bisacsh Darstellungstheorie; lineare Transformationen; Vektorräume; Geometrie Polynomial representations; orbital varieties; Kazhdan–Lusztig polynomials; Hecke algebra; Lusztig–Vogan polynomials; pattern avoidance Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-076694-3 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-076696-7 De Gruyter Studies in Mathematics Volume 90 (DE-604)BV000005407 90 B:DE-101 application/pdf https://d-nb.info/1265199779/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034006289&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | McGovern, William M. 1959- Representation theory and geometry of the flag variety De Gruyter Studies in Mathematics Darstellungstheorie Geometrie Vektorräume lineare Transformationen MATHEMATICS / Algebra / General bisacsh |
| title | Representation theory and geometry of the flag variety |
| title_auth | Representation theory and geometry of the flag variety |
| title_exact_search | Representation theory and geometry of the flag variety |
| title_exact_search_txtP | Representation theory and geometry of the flag variety |
| title_full | Representation theory and geometry of the flag variety William M. McGovern |
| title_fullStr | Representation theory and geometry of the flag variety William M. McGovern |
| title_full_unstemmed | Representation theory and geometry of the flag variety William M. McGovern |
| title_short | Representation theory and geometry of the flag variety |
| title_sort | representation theory and geometry of the flag variety |
| topic | Darstellungstheorie Geometrie Vektorräume lineare Transformationen MATHEMATICS / Algebra / General bisacsh |
| topic_facet | Darstellungstheorie Geometrie Vektorräume lineare Transformationen MATHEMATICS / Algebra / General |
| url | https://d-nb.info/1265199779/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034006289&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005407 |
| work_keys_str_mv | AT mcgovernwilliamm representationtheoryandgeometryoftheflagvariety AT walterdegruytergmbhcokg representationtheoryandgeometryoftheflagvariety |
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