Book Review: The representation theory of the symmetric group
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چکیده
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15 صفحه اولRepresentation Theory of the Symmetric Group
Remark 1.2. The definition of an FG-module is more technical than the definition of a representation of G, but, as the exercise shows, the two notions are equivalent. Module can be more convenient to work with, because there is less notation, and we can use results from ring theory without any translation. The language of representations is preferable if we want to have an explicit map ρ : G→ G...
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We show how voting may be viewed naturally from an algebraic perspective by viewing voting profiles as elements of certain well-studied QSn-modules. By using only a handful of simple combinatorial objects (e.g., tabloids) and some basic ideas from representation theory (e.g., Schur's Lemma), this allows us to recast and extend some well-known results in the field of voting theory.
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from 1950s onward, new theories and critical approaches burgeoned across humanities. these theories were context-oriented; as a result, the analysis of discursive practices gained significance. thus, social, political, historical and cultural discourses that have been hitherto marginalized and considered inferior to literary texts, were introduced as important texts to be analyzed by critics. o...
“Frobenius twists” in the representation theory of the symmetric group
For the general linear group GLn(k) over an algebraically closed field k of characteristic p, there are two types of “twisting” operations that arise naturally on partitions. These are of the form λ → pλ and λ → λ+ prτ The first comes from the Frobenius twist, and the second arises in various tensor product situations, often from tensoring with the Steinberg module. This paper surveys and adds ...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1983
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1983-15121-2