Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1979. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Vita. / Bibliography: leaves 163-165. / Ph.D.

Esta tese consiste em um estudo das representações do islã, de árabes e muçulmanos veiculadas pela telenovela O Clone. Seu objetivo principal é verificar como a novela levou a cultura islâmica para a televisão na conjuntura do imediato pós 11 de setembro de 2001. Utilizando como fonte principal o discurso presente na telenovela, concluímos que O Clone funcionou como um instrumento didático para as audiências, oferecendo informações da cultura e religião islâmica em um momento em que essa tradição cultural era bastante estigmatizada. A novela, apesar de reiterar algumas caricaturas e de generalizações decorrentes acima de tudo de sua natureza folhetinesca-melodramática, ofereceu representações positivas oportunizando uma leitura mais humanizada do Outro muçulmano. Concluímos também que O Clone levou para a televisão elementos que estão presentes no contexto contemporâneo e que impregna as relações do Oriente islâmico com o mundo moderno e o Ocidente. Identificamos que a telenovela também ofereceu um retrato dos dilemas que atravessam a contemporaneidade islâmica. Por fim, percebemos também que o folhetim eletrônico de Glória Perez se utilizou do recurso intertextual ao levar representações, ideias e imagens já estabelecidas na tradição literária orientalista derivada das Mil e Uma Noites e suas adaptações e reelaborações. Através do primado da orientalidade, um acervo de imagens canônicas sobre o Oriente, possibilitou uma rápida identificação do público com um antigo imaginário, já estabelecido e bastante familiar para uma população que assiste TV. / This thesis is based in a study of representations of Islam, Arabs and muslins broadcast by the soap opera O Clone (The Clone). Its primary goal is to verify how the soap opera carried the Islamic culture to the post 9/11 television. Using as a primary source the discourse present in the soap opera, we concluded that O Clone has worked as a didactic instrument for the audiences, offering information from the Islamic culture and religion in a moment in which such cultural tradition was quite stigmatized. The soap opera, despite the reuse of some caricature and generalization derived, foremost, from its feuilletonistic-melodramatic nature, managed to offer positive representations enabling a more humanized reading of the muslim Other. We conclude, as well, that O Clone has brought to television elements that are present in the contemporary context and pervade the Eastern Islamic relations with the modern world and the West. We could also identify that Gloria Perezs electronic feuilleton made use of the intertextual asset by leading representations, ideas and images already settled in the orientalist literary tradition derived from the The Thousand and One Nights and its adaptations and revisions. Through the primacy of orientality, a pile of canonic images about the East, made possible a fast identification of the public with a ancient imaginary, previously settled and very familiar to a population that watches TV.

We can view quiver representations of a fixed dimension vector as an algebraic variety over an algebraically closed field $K$. There is an action of the product of general linear groups on each of these varieties where the orbits of the action correspond to isomorphism classes of quiver representation. A $K$-algebra $A$ is said to have the dense orbit property if for each dimension vector, the product of the general linear group acts on each irreducible component of the module variety with a dense orbit. Under certain conditions, a $K$ algebra $A$ is representation finite if and only if it $A$ has the dense orbit property. The implication representation finite implies the dense orbit property is always true. The converse is not true in general, as shown by Chindris, Kinser, and Weyman in \cite{ryan}. Our main theorem of this thesis builds on their work to give a family of representation infinite algebras with the dense orbit property. We also give a conjectured classification of indecomposables with dense orbits. \par In the future, we hope the work presented here can be used to find even more examples of representation infinite algebra with the dense orbit property to then develop deeper theory to classify algebras with the dense orbit property that are representation infinite.

Irreducible representations of a finite group over a field are important because all representations of a group are direct sums of irreducible representations. Maschke tells us that if φ is a representation of the finite group G of order n on the m-dimensional space V over the field K of complex numbers and if U is an invariant subspace of φ, then U has a complementary reducing subspace W . The objective of this thesis is to find all irreducible representations of the dihedral group D2n. The reason we will work with the dihedral group is because it is one of the first and most intuitive non-abelian group we encounter in abstract algebra. I will compute the representations and characters of D2n and my thesis will be an explanation of these computations. When n = 2k + 1 we will show that there are k + 2 irreducible representations of D2n, but when n = 2k we will see that D2n has k + 3 irreducible rep- resentations. To achieve this we will first give some background in group, ring, module, and vector space theory that is used in representation theory. We will then explain what general representation theory is. Finally we will show how we arrived at our conclusion.

We construct an algorithm for getting a reduced expression for any element in a complex reflection group G(m, 1, r) by sorting the element, which is in the form of a sequence of complex numbers, to the identity. Thus, the algorithm provides us a set of reduced expressions, one for each element. We establish a one-one correspondence between the set of all reduced expressions for an element and a set of certain sorting sequences which turn the element to the identity. In particular, this provides us with a combinatorial method to check whether an expression is reduced. We also prove analogues of the exchange condition and the strong exchange condition for elements in a G(m, 1, r). A Bruhat order on the groups is also defined and investigated. We generalize the Geck-Pfeiffer reducibility theorem for finite Coxeter groups to the groups G(m, 1, r). Based on this, we prove that a character value of any element in an Ariki-Koike algebra (the Hecke algebra of a G(m, 1, r)) can be determined by the character values of some special elements in the algebra. These special elements correspond to the reduced expressions, which are constructed by the algorithm, for some special conjugacy class representatives of minimal length, one in each class. Quasi-parabolic subgroups are introduced for investigating representations of Ariki- Koike algebras. We use n x n arrays of non-negative integer sequences to characterize double cosets of quasi-parabolic subgroups. We define an analogue of permutation modules, for Ariki-Koike algebras, corresponding to certain subgroups indexed by multicompositions. These subgroups are naturally corresponding, not necessarily one-one, to quasi-parabolic subgroups. We prove that each of these modules is free and has a basis indexed by right cosets of the corresponding quasi-parabolic subgroup. We also construct Murphy type bases, Specht series for these modules, and establish a Young's rule in this case.

Représentations des groupes de Lie conformes et quantification des espaces symétriques

Over the last few decades increasing rates of single mother households in the United States have triggered a national alarm over the effects of father absence on society. Father absence has been linked specifically to many of the problems plaguing black communities in the United States (e.g. poverty, low educational attainment, etc.) and as a result community and political leaders alike have consistently promoted responsible fatherhood practices as a way to address them. Although responsible fatherhood has received, in this context, a considerable amount of social attention, this attention has come intertwined with considerable political and moral rhetoric at all levels, making an idea invested with a wide variety of often-conflicting meanings and interests. <br>Given the paucity of academic studies giving voice to black fathers at the metaphoric "front line" of the national responsible fatherhood effort, this author used a variation of The Listening Guide (Gilligan 2003) to capture the narratives of four black fathers volunteering in a local responsible fatherhood program. Critical Social Representations Theory was used to frame the interaction between participants and the social contexts within which they are embedded, paying particular attention to participants' positioning in regard to social representations of race and gender. The widely different understandings of fatherhood present within the results point to fatherhood as a highly dynamic concept. Responsibility, on the other hand, was understood primarily as father presence, a middle class ideal that I argue is problematic given the realities of poor black fathers. Finally, all fathers tended to resist ideas of race as essence, even if in regard to gender all fathers adopted hegemonic positions endorsing views of gender difference as essential and as grounded in biology. Overall, results reveal complex portrayals of black fathers and their lives in communities where race, poverty, incarceration, drugs, violence, or family court all pose additional challenges to responsible fatherhood. / McAnulty College and Graduate School of Liberal Arts / Clinical Psychology / PhD / Dissertation

Most reinforcement learning methods operate on propositional representations of the world state. Such representations are often intractably large and generalize poorly. Using a deictic representation is believed to be a viable alternative: they promise generalization while allowing the use of existing reinforcement-learning methods. Yet, there are few experiments on learning with deictic representations reported in the literature. In this paper we explore the effectiveness of two forms of deictic representation and a naive propositional representation in a simple blocks-world domain. We find, empirically, that the deictic representations actually worsen performance. We conclude with a discussion of possible causes of these results and strategies for more effective learning in domains with objects.

In 1992, Xiao-Song Lin constructed an invariant h of knots in the 3-sphere via a signed count of the conjugacy classes of irreducible SU(2)-representations of the fundamental group of the knot exterior with trace-free meridians. Lin showed that h equals one-half times the knot signature. Using methods similar to Lin's, we construct an invariant of two-component links in the 3-sphere. Our invariant is a signed count of conjugacy classes of projective SU(2)-representations of the fundamental group of the link exterior with a fixed 2-cocycle and corresponding non-trivial second Stiefel--Whitney class. We show that our invariant is, up to a sign, the linking number. We further construct, for a two-component link in an integral homology sphere, an instanton Floer homology whose Euler characteristic is, up to sign, the linking number between the components of the link. We relate this Floer homology to the Kronheimer-Mrowka instanton Floer homology of knots. We also show that, for two-component links in the 3-sphere, the Floer homology does not vanish unless the link is split.

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