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Quantum linear groups and representations of GLn (Fq) /
We give a self-contained account of the results originating in the work of James and the second author in the 1980s relating the representation theory of GL[n(F[q) over fields of characteristic coprime to q to the representation theory of "quantum GL[n" at roots of unity. The new treatment...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence, R.I. :
American Mathematical Society,
©2001.
|
| Colección: | Memoirs of the American Mathematical Society ;
no. 706. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Brundan, Jonathan, |d 1970- |1 https://id.oclc.org/worldcat/entity/E39PCjx4cpffRkkcvpQqbBvkfy | |
| 245 | 1 | 0 | |a Quantum linear groups and representations of GLn (Fq) / |c Jonathan Brundan, Richard Dipper, Alexander Kleshchev. |
| 260 | |a Providence, R.I. : |b American Mathematical Society, |c ©2001. | ||
| 300 | |a 1 online resource (viii, 112 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 490 | 1 | |a Memoirs of the American Mathematical Society, |x 1947-6221 ; |v v. 706 | |
| 500 | |a "January 2001, Volume 149, Number 706 (first of 4 numbers)." | ||
| 504 | |a Includes bibliographical references. | ||
| 588 | 0 | |a Print version record. | |
| 520 | 8 | |a We give a self-contained account of the results originating in the work of James and the second author in the 1980s relating the representation theory of GL[n(F[q) over fields of characteristic coprime to q to the representation theory of "quantum GL[n" at roots of unity. The new treatment allows us to extend the theory in several directions. First, we prove a precise functorial connection between the operations of tensor product in quantum GL[n and Harish-Chandra induction in finite GL[n. This allows us to obtain a version of the recent Morita theorem of Cline, Parshall and Scott valid in addition for p-singular classes. From that we obtain simplified treatments of various basic known facts, such as the computation of decomposition numbers and blocks of GL[n(F[q) from knowledge of the same for the quantum group, and the non-defining analogue of Steinberg's tensor product theorem. We also easily obtain a new double centralizer property between GL[n(F[[q) and quantum GL[n, generalizing a result of Takeuchi. Finally, we apply the theory to study the affine general linear group, following ideas of Zelevinsky in characteristic zero. We prove results that can be regarded as the modular analogues of Zelevinsky's and Thoma's branching rules. Using these, we obtain a new dimension formula for the irreducible cross-characteristic representations of GL[n(F[q), expressing their dimensions in terms of the characters of irreducible modules over the quantum group | |
| 505 | 0 | 0 | |t Introduction |t 1. Quantum linear groups and polynomial induction |t 2. Classical results on $GL_n$ |t 3. Connecting $GL_n$ with quantum linear groups |t 4. Further connections and applications |t 5. The affine general linear group. |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Linear algebraic groups. | |
| 650 | 0 | |a Representations of groups. | |
| 650 | 0 | |a Group schemes (Mathematics) | |
| 650 | 6 | |a Groupes linéaires algébriques. | |
| 650 | 6 | |a Représentations de groupes. | |
| 650 | 6 | |a Schémas en groupes. | |
| 650 | 7 | |a Group schemes (Mathematics) |2 fast | |
| 650 | 7 | |a Linear algebraic groups |2 fast | |
| 650 | 7 | |a Representations of groups |2 fast | |
| 700 | 1 | |a Dipper, Richard. | |
| 700 | 1 | |a Kleshchëv, A. S. |q (Aleksandr Sergeevich) |1 https://id.oclc.org/worldcat/entity/E39PCjHYcF6vgmxVjYYtJbk343 | |
| 776 | 0 | 8 | |i Print version: |a Brundan, Jonathan, 1970- |t Quantum linear groups and representations of GLn (Fq) / |x 0065-9266 |z 9780821826164 |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 706. |x 0065-9266 | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=3114411 |z Texto completo |
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