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The following thesis explores an extension to the classical McKay correspondence, a theorem that touches on several areas of mathematics. Our extension comes by considering pseudo reflection groups which were not included in the original correspondence. The discriminant of a pseudo reflection group is a singular hypersurface expressed by a polynomial ∆ in the invariant ring of the group action. A main object of study is the matrix factorization (z, j) of ∆, and the corresponding Cohen-Macaulay module, arising from the arrangement of the hyperplanes fixed by the reflections. A key idea that we frequently use is that the matrix factorization (z, j) can be decomposed using the irreducible representations of the group. A McKay correspondence of refection groups generated by reflections of order 2 has been presented by Buchweitz-Faber-Ingalls. In Chapter 3 we follow the methods from Loc. cit and consider the complex reflection groups G(m, p,2), which appear in the Shephard-Todd classification and show that similar results hold. The matrix factorization is fully decomposed and the corresponding decomposition of the Cohen-Macaulay module is given. A collaboration with Eleonore Faber, Colin Ingalls and Marco Talarico has resulted in a description of the decomposition of the matrix factorization (z, j) of ∆ for the symmetric group Sn on n letters. In Chapter 4 a modification of higher Specht polynomials is used to present a computational way to explicitly calculate the decomposition of the corresponding Cohen-Macaulay module of (z, j). In Chapter 5, the Lusztig algebra for the pseudo reflection group G(m,1,2) which is Morita equivalent algebra to the skew group ring is calculated. This is achieved by using the McKay quivers for G(m,1,2) and calculating the required relations in terms of 2-paths. The Lusztig algebra can give us insights into how the McKay correspondence can generalise to pseudo reflection groups.

The current literature on mafia transplantation into the US does not address the relationship between Italian mafia groups and United States mafia groups in the pre-prohibition era; any connection between the two is assumed rather than proven. This thesis argues that mafia transplantation theory, showing that the operation of an overseas outpost by an Italian mafia is insufficient in explaining the movement of mafiosi from Italy to the United States and the formation of groups in the United States. Instead, it suggests that members of groups in the United States used knowledge obtained in Italy, but in the form of imitation rather than control. This imitation was based on elements of cultural heritage with which the mafioso would be familiar, helping define the structure, relationships, rituals and modus operandi of the US groups. The research involved examining records from various archives; newspaper, police, immigration records, personal records, etc., in order to find proof of transplantation outposts operations, influence or of home-grown mafia. The thesis tackles transplantation in three areas; migration, markets and operations. It shows that generalised migration was not a factor in determining the transplantation of a mafia group and shows that individual Mafiosi travelled often as the result of increased law enforcement efforts against them rather than as part of a strategy. The thesis demonstrates that the markets in which these migrated Mafiosi operated in the United States were not comparable in a way that suggests the running of an outpost from Italy, but instead that these mafiosi's groups adapted to changing conditions in the United States. At an operational level, the groups in the US fed off the reputation of their Italian counterparts but were imitating their practices rather than being subservient to their control. Overall the thesis shows that the Mafia groups in the US were not operating as an outpost under control of an Italian organisation and instead were made up of close affiliations of individuals with the relevant skills to take advantage of and adapt to the local American conditions in a form influenced by their Italian counterparts.

Focusing on the works of Christopher Marlowe (1564-93), this thesis explores the complex engagement of popular drama with the political and religious writing of the Elizabethan fin de siècle. It focuses on the five plays by Marlowe that feature royal protagonists: 1-2 Tamburlaine (1587), Dido, Queen of Carthage (1588), Edward II (1592), and The Massacre at Paris (1593). By interpreting each play in its immediate political context, it shows that Marlowe did not deal with monarchy in the abstract but responded to current affairs - from the incursions of the Ottoman Empire to the threat of the Spanish Armada, from the conspiracy claims of Catholic polemic to the debate surrounding England's involvement in continental warfare. The introduction situates the thesis in the critical and historiographical context relating to Marlowe and to the relationship between literature and politics in the early modern period; it provides the justification for reading Marlowe's plays as topical statements. Chapter One looks at 1-2 Tamburlaine in the light of contemporary attitudes to the Ottoman-Safavid War. Chapter Two shows that Dido, Queen of Carthage adapted the stories and tropes of polemic to reflect fears of Catholic conspiracy and Spanish invasion. Chapter Three reads Edward II as a creative response to the print war of 1591-2, which centred on the moral character of the queen's closest counsellors. Chapter Four proposes that Marlowe's final play, The Massacre at Paris, employed arguments drawn from Reason of State to influence decisions at the 1593 Parliament. The thesis concludes by suggesting that despite Marlowe's reputation as a radical overreacher, his drama displays considerable sympathy for the monarchs who must rule precariously and without the option of private happiness.