The thrust of this thesis is to describe base change BC_E/F at the level of chamber homology and K-theory for some p-adic groups, such as SL(2,F), GL(1,F) and GL(2,F). Here F is a non-archimedean local field and E is a Galois extension of F. We have had to master the representation theory of SL(2) and GL(2) including the Langlands parameters. The main result is an explicit computation of the effect of base change on the chamber homology groups, each of which is constructed from cycles. This will have an important connection with the Baum-Connes correspondence for such p-adic groups. This thesis involved the arithmetic of fields such as E and F, geometry of trees, the homology groups and the Weil group W_F.

This thesis consists of four papers about the intersection between semigroup theory, category theory and representation theory. We say that a representation of a semigroup by a matrix semigroup is effective if it is injective and define the effective dimension of a semigroup S as the minimal n such that S has an effective representation by square matrices of size n. A multisemigroup is a generalization of a semigroup where the multiplication is set-valued, but still associative. A 2-category consists of objects, 1-morphisms and 2-morphisms. A finitary 2-category has finite dimensional vector spaces as objects and linear maps as morphisms. This setting permits the notion of indecomposable 1-morphisms, which turn out to form a multisemigroup. Paper I computes the effective dimension Hecke-Kiselman monoids of type A. Hecke-Kiselman monoids are defined by generators and relations, where the generators are vertices and the relations depend on arrows in a given quiver. Paper II computes the effective dimension of path semigroups and truncated path semigroups. A path semigroup is defined as the set of all paths in a quiver, with concatenation as multiplication. It is said to be truncated if we introduce the relation that all paths of length N are zero. Paper III defines the notion of a multisemigroup with multiplicities and discusses how it better captures the structure of a 2-category, compared to a multisemigroup (without multiplicities). Paper IV gives an example of a family of 2-categories in which the multisemigroup with multiplicities is not a semigroup, but where the multiplicities are either 0 or 1. We describe these multisemigroups combinatorially.

This thesis aims to describe how Western tourist websites represents India. Although there has been much research on tourism and Western representation of India, no literature is available on how Western tourist websites represents India. This thesis uses three theories, social constructivism, post-colonial theory, and representation theory. Social constructivism is the base for this thesis. Post-colonial theory is used to find out whether the representation of India includes colonial stereotypes or no. Moreover, the representation theory is the center and the main tool to know and explain how Western tourist websites represents India. The design used is a 'case study' as case study design is compatible to explore the representations of India. The method used is a 'qualitative discourse analysis' which helps to provide a critical analysis of the description of India. Main results of this thesis are that Western tourist websites describe Indian economy as a backward economy. It is unclear whether Indian politics is described as undemocratic or democratic. Indian people are described as a mix of traditional, modern, unfree as well as free people. Indian culture is described as ancient and collective.

Root systems are a fundamental concept in the theory of Lie algebra. In this thesis, we will use two different kind of graphs to represent the group generated by reflections acting on the elements of the root system. The root systems we are interested in are those of type A2, B2 and G2. After drawing the graphs, we will study the algebraic groups corresponding to those root systems. We will use three different techniques to give a geometric description of the homogeneous spaces G/P where G is the algebraic group corresponding to the root system and P is one of its parabolic subgroup. Finally, we will make a link between the graphs and the multiplication of basis elements in the Chow group CH(G/P).

The realizations of the basic representation of the affine general linear Lie algebra on (r x r) matrices are well-known to be parametrized by partitions of r and have an explicit description in terms of vertex operators on the bosonic/fermionic Fock space. In this thesis, we give a geometric interpretation of these realizations in terms of geometric operators acting on the equivariant cohomology of certain Nakajima quiver varieties.

Media is responsible to operate as a room for democratic and interacting discussions in our society. Furthermore, media is a significant part of the overall social context in which citizens are included. Despite increased equality in society, the media still represents women and men unequal which has an impact on the norms and values that prevail in society. Women are still underrepresented in Swedish media content and women’s perspectives and experiences are either marginalized or lacking. This thus confirms and reproduces a society and power structure in which men are superior to women. Further entrepreneurship is critical as it contributes with economic growth and social development and therefore of value for society and politics.  The aim of this study is to examine how women’s entrepreneurship is represented in Framgångspodden and how this podcast discursively constructs gender. The research questions build upon previous studies that show how female entrepreneurs are represented and portrayed differently than male entrepreneurs. Furthermore, the representation of women’s entrepreneurship is gender stereotypical where masculine and feminine characteristics are contrasted. Previous studies also show how the entrepreneurship field is severe to unequal power relations and how female entrepreneurs are diminished.    Through a thematic and critical discourse analysis this study examines how 13 Swedish female entrepreneurs are represented in Framgångspodden. The conclusion of this qualitative study validates previous studies and shows how gender stereotypes exist in a Swedish entrepreneurial context and that the discourse is dominated by a distinct order of power. Framgångspodden defends the masculine entrepreneurship discourse and reproduces the image of how a female entrepreneur should behave or be, by describing her with feminine qualities or placing her in a narrow spectrum of masculine stereotypes. This study confirms that the women's entrepreneurship discourse in Sweden is characterized by masculinity and female entrepreneurs are represented based on their gender roles.

We define a faithful linear monoidal functor from the partition category, and hence from Deligne's category Rep(S_t), to the additive Karoubi envelope of the Heisenberg category. We show that the induced map on Grothendieck rings is injective and corresponds to the Kronecker coproduct on symmetric functions. We then generalize the above results to any group G, the case where G is the trivial group corresponding to the case mentioned above. Thus, to every group G we associate a linear monoidal category Par(G) that we call a group partition category. We give explicit bases for the morphism spaces and also an efficient presentation of the category in terms of generators and relations. We then define an embedding of Par(G) into the group Heisenberg category associated to G. This embedding intertwines the natural actions of both categories on modules for wreath products of G. Finally, we prove that the additive Karoubi envelope of Par(G) is equivalent to a wreath product interpolating category introduced by Knop, thereby giving a simple concrete description of that category.

I följande arbete kombineras Social Representation Theory (SRT) med kvantitativ innehållsanalys när politiska facebookgrupper undersöks. Fyra grupper och tolv inlägg och 164 kommentarer undersöks. Den kvantitativa innehållsanalysen visar att samtalsklimatet på politiska facebookgrupper är hårt och ganska elakt. Dessutom präglas grupperna av en viss enhällighet vad gäller åsikter och en av fyra grupper bedöms vara en ekokammare. SRT-analysen undersöker sociala representationer och visar att strategin objektifiering är den som förekommer oftast på politiska facebookgrupper. Objektifiering handlar om att göra det okända känt genom förenklande jämförelser. I exempelvis diskussioner om Sveriges covid-19 strategi så jämförs äldre svenskar med offerlamm i ett försök att kritisera Sveriges covid-19 strategi. Objektifiering förekommer även när socialism som ideologi kritiseras genom att likställas med kommunism. En annan SRT-strategi som förekom ofta var motsats förankring, vilket innebär att grupper ställs mot varandra, som när gruppen papperslösa invandrare (ej att tycka synd om) jämfördes med fattigpensionärer (att tycka synd om). / In the following work, Social Representation Theory (SRT) is combined with quantitative content analysis when political Facebook groups are examined. Four groups and twelve posts and 164 comments are examined. The quantitative content analysis shows that the conversational climate on political Facebook groups is harsh and rather nasty. In addition, the groups are characterized by a certain unanimity in terms of opinions and one in four groups is judged an echo chamber. The SRT analysis examines social representations and shows that the objectification strategy is the one that most often occurs on political Facebook groups. Objectification is about making the unknown known through simplifying comparisons. In discussions about Sweden's covid-19 strategy, for example, older Swedes are compared to sacrificial lambs in an attempt to criticize Sweden's covid-19 strategy. Objectification also occurs when socialism as an ideology is criticized by being equated with communism. Another SRT strategy that often occurred was opposing anchoring, which means that groups are pitted against each other, as when the group of undocumented immigrants (not to feel sorry for) was compared to poor pensioners (to feel sorry for).

This study examines how The Swedish Armed Forces (SAF) communicates via their commercials and how this may affect their brand. The Swedish Armed Forces has always been an important authority and their priority is to prevent war and crisis in Swedish society. According to SAF themselves, one of their strategies with using commercials frequently is to attract potential recruits. Even though this is their goal, the SAF hasn't always been as open minded as today. In fact it’s been a relatively closed authority in earlier years, according to previous research. This has created a lack of knowledge among the public regarding what they do. This study compares two time periods to see if their commercials have changed. The first time period extends from 2011 until 2016 and the second period extends from 2017 to 2022. The theories that are applied to this study are semiotics, framing and representation theory and the methods that are used are a quantitative content analysis and a semiotic analysis. By using these theories and methods it might be possible to discover similarities and differences in the commercials and also to seek for a greater meaning in the empirical material. The reason why this topic is interesting to research is because the SAF is one of the most important authorities in Sweden and also because Sweden re-introduced compulsory conscription in 2017. Because of that it is of importance that the SAF appears as an attractive brand and a good employer. The result of the study states that the commercials have developed a lot over years and that they nowadays exhibit several parts within the SAF and that they represent diversity. In earlier years only one type of human was represented in their films but by the years they have included humans with different ethnicities, gender, sexuality and lifestyles within their films. They also show parallels between daily life and the life within the armed forces. By doing this they appear to be closer to the people which creates a feeling of safety and importance towards their work.

Superconformal field theories (SCFTs) are an important class of quantum field theories. These SCFTs have been a significant component in exploring and comprehending the fundamental framework of quantum field theories. In the vast realm of quantum field theories, integrability plays a crucial role, providing powerful analytic tools that allow us to solve certain physical quantities exactly. In this thesis, we focus on the representation theory of the algebraic structure in six-dimensional (6D) SCFTs and investigate the intricate interplay between 6D SCFTs and integrability. To begin, we delve into the fundamental concepts of representation theory, establishing a solid foundation for our subsequent analysis. The discussion then will move on to all possible generators in the SCFTs, explaining how they are realized in terms of bosonic and fermionic oscillators. Finally, we investigate spin chains and their application in 6D SCFTs. We demonstrate that symmetry arguments derived from representation theory are not sufficient to establish the integrability of the spin chains in 6D SCFTs. This conclusion does not imply the absence of integrable systems within 6D SCFTs; rather, it suggest there are other potential methods available e.g., correlation functions, to explore the appearance of integrable systems in 6D SCFTs. / Superkonforma fältteorier (SCFTs) är en viktig klass av kvantfältteorier. Dessa SCFTs utgör en viktig komponent för att utforska och förstå det fundamentala ramverket för kvantfältteorin. Inom det stora riket av kvantfältteori spelar integrabilitet en avgörande roll, vilket tillhandahåller kraftfulla analytiska verktyg som gör att vi kan lösa vissa fysiska storheter exakt. I denna avhandling fokuserar vi på representationsteorin av den algebraiska strukturen i sexdimensionella (6D) SCFTs och undersöker det intrikat samspelet mellan 6D SCFTs och integrabilitet. Till att börja med kommer vi att fördjupa oss i de grundläggande begreppen inom representationsteori och skapa en gedigen grund för vår efterföljande analys.  Diskussionen kommer sedan att gå vidare till alla möjliga generatorer i SCFTs, och förklarar hur de realiseras i termer av bosoniska och fermioniska oscillatorer. Slutligen kommer spinnkedjor och dess tillämpningar i 6D SCFTs att undersökas. Vi kommer visa att symmetriargument som härleds från representationsteori inte är  tillräckliga för att fastställa integrerbarhet av spinnkedjor i 6D SCFTs. Denna slutsats innebär inte att integrerbara system inte existerar inom 6D SCFTs, utan föreslår att det finns andra potentiella metoder, till exempel korrelationsfunktioner, för att utforska existensen av integrerbara system i 6D SCFTs.