Quantum Linear Groups and Representations of GL n mathbb F q is popular PDF and ePub book, written by Jonathan Brundan in 2001, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Quantum Linear Groups and Representations of GL n mathbb F q can be Read Online from any device for your convenience.
Quantum Linear Groups and Representations of GL n mathbb F q Book PDF Summary
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.
Detail Book of Quantum Linear Groups and Representations of GL n mathbb F q PDF
- Author : Jonathan Brundan
- Release : 01 October 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821826164
- Genre : Mathematics
- Total Page : 127 pages
- Language : English
- PDF File Size : 8,9 Mb
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