Discrete series of GLn over a finite field:
In this book Professor Lusztig solves an interesting problem by entirely new methods: specifically, the use of cohomology of buildings and related complexes.The book gives an explicit construction of one distinguished member, D(V), of the discrete series of GLn (Fq), where V is the n-dimensional F-v...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Princeton, NJ
Princeton University Press
1974
|
| Series: | Annals of Mathematics Studies
number 81 |
| Subjects: | |
| Online Access: | Volltext |
| Summary: | In this book Professor Lusztig solves an interesting problem by entirely new methods: specifically, the use of cohomology of buildings and related complexes.The book gives an explicit construction of one distinguished member, D(V), of the discrete series of GLn (Fq), where V is the n-dimensional F-vector space on which GLn(Fq) acts. This is a p-adic representation; more precisely D(V) is a free module of rank (q--1) (q2—1)...(qn-1—1) over the ring of Witt vectors WF of F. In Chapter 1 the author studies the homology of partially ordered sets, and proves some vanishing theorems for the homology of some partially ordered sets associated to geometric structures. Chapter 2 is a study of the representation △ of the affine group over a finite field. In Chapter 3 D(V) is defined, and its restriction to parabolic subgroups is determined. In Chapter 4 the author computes the character of D(V), and shows how to obtain other members of the discrete series by applying Galois automorphisms to D(V). Applications are in Chapter 5. As one of the main applications of his study the author gives a precise analysis of a Brauer lifting of the standard representation of GLn(Fq) |
| Item Description: | Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) |
| Physical Description: | 1 online resource |
| ISBN: | 9781400881765 |
| DOI: | 10.1515/9781400881765 |
Staff View
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| 490 | 1 | |a Annals of Mathematics Studies |v number 81 | |
| 500 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) | ||
| 520 | |a In this book Professor Lusztig solves an interesting problem by entirely new methods: specifically, the use of cohomology of buildings and related complexes.The book gives an explicit construction of one distinguished member, D(V), of the discrete series of GLn (Fq), where V is the n-dimensional F-vector space on which GLn(Fq) acts. This is a p-adic representation; more precisely D(V) is a free module of rank (q--1) (q2—1)...(qn-1—1) over the ring of Witt vectors WF of F. In Chapter 1 the author studies the homology of partially ordered sets, and proves some vanishing theorems for the homology of some partially ordered sets associated to geometric structures. Chapter 2 is a study of the representation △ of the affine group over a finite field. In Chapter 3 D(V) is defined, and its restriction to parabolic subgroups is determined. In Chapter 4 the author computes the character of D(V), and shows how to obtain other members of the discrete series by applying Galois automorphisms to D(V). Applications are in Chapter 5. As one of the main applications of his study the author gives a precise analysis of a Brauer lifting of the standard representation of GLn(Fq) | ||
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| id | DE-604.BV043712436 |
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| indexdate | 2024-07-10T07:33:08Z |
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| isbn | 9781400881765 |
| language | English |
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| spelling | Lusztig, George 1946- (DE-588)118813730 aut Discrete series of GLn over a finite field George Lusztig Princeton, NJ Princeton University Press 1974 © 1974 1 online resource txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 81 Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) In this book Professor Lusztig solves an interesting problem by entirely new methods: specifically, the use of cohomology of buildings and related complexes.The book gives an explicit construction of one distinguished member, D(V), of the discrete series of GLn (Fq), where V is the n-dimensional F-vector space on which GLn(Fq) acts. This is a p-adic representation; more precisely D(V) is a free module of rank (q--1) (q2—1)...(qn-1—1) over the ring of Witt vectors WF of F. In Chapter 1 the author studies the homology of partially ordered sets, and proves some vanishing theorems for the homology of some partially ordered sets associated to geometric structures. Chapter 2 is a study of the representation △ of the affine group over a finite field. In Chapter 3 D(V) is defined, and its restriction to parabolic subgroups is determined. In Chapter 4 the author computes the character of D(V), and shows how to obtain other members of the discrete series by applying Galois automorphisms to D(V). Applications are in Chapter 5. As one of the main applications of his study the author gives a precise analysis of a Brauer lifting of the standard representation of GLn(Fq) In English Algebraic fields Linear algebraic groups Representations of groups Series Diskrete Reihe (DE-588)4150181-0 gnd rswk-swf Ordnung n (DE-588)4322729-6 gnd rswk-swf Lineare Gruppe (DE-588)4138778-8 gnd rswk-swf Lineare Gruppe (DE-588)4138778-8 s Ordnung n (DE-588)4322729-6 s Diskrete Reihe (DE-588)4150181-0 s 1\p DE-604 Erscheint auch als Druck-Ausgabe 0-691-08154-9 Annals of Mathematics Studies number 81 (DE-604)BV040389493 81 https://doi.org/10.1515/9781400881765?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lusztig, George 1946- Discrete series of GLn over a finite field Annals of Mathematics Studies Algebraic fields Linear algebraic groups Representations of groups Series Diskrete Reihe (DE-588)4150181-0 gnd Ordnung n (DE-588)4322729-6 gnd Lineare Gruppe (DE-588)4138778-8 gnd |
| subject_GND | (DE-588)4150181-0 (DE-588)4322729-6 (DE-588)4138778-8 |
| title | Discrete series of GLn over a finite field |
| title_auth | Discrete series of GLn over a finite field |
| title_exact_search | Discrete series of GLn over a finite field |
| title_full | Discrete series of GLn over a finite field George Lusztig |
| title_fullStr | Discrete series of GLn over a finite field George Lusztig |
| title_full_unstemmed | Discrete series of GLn over a finite field George Lusztig |
| title_short | Discrete series of GLn over a finite field |
| title_sort | discrete series of gln over a finite field |
| topic | Algebraic fields Linear algebraic groups Representations of groups Series Diskrete Reihe (DE-588)4150181-0 gnd Ordnung n (DE-588)4322729-6 gnd Lineare Gruppe (DE-588)4138778-8 gnd |
| topic_facet | Algebraic fields Linear algebraic groups Representations of groups Series Diskrete Reihe Ordnung n Lineare Gruppe |
| url | https://doi.org/10.1515/9781400881765?locatt=mode:legacy |
| volume_link | (DE-604)BV040389493 |
| work_keys_str_mv | AT lusztiggeorge discreteseriesofglnoverafinitefield |