Application of group representation theory to symmetric structures
نویسندگان
چکیده
منابع مشابه
Representation 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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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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Partitions can be graphically represented by Young frames, which are Young tableaux with empty boxes. The i-th part λi corresponds to the i-th row of the frame, consisting of λi boxes. Conversely, the Young frames of n boxes can be uniquely labelled by a partition λ ` n. We will therefore identify a Young frame with the partition labelling it. A Young tableau (YT) of N objects and of shape λ ` ...
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This paper is a survey of some of the ways in which the representation theory of the symmetric group has been used in voting theory and game theory. In particular, we use permutation representations that arise from the action of the symmetric group on tabloids to describe, for example, a surprising relationship between the Borda count and Kemeny rule in voting. We also explain a powerful repres...
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ژورنال
عنوان ژورنال: Applied Mathematical Modelling
سال: 1981
ISSN: 0307-904X
DOI: 10.1016/s0307-904x(81)80082-0