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We associate a sign to F-stable reductive subgroups of a reductive group with a Frobenius root F, and define Curtis–Alvis duality. We prove its properties, in particular commutation with Harish–Chandra induction and to restriction to centralisers of semi-simple elements. We define the Steinberg character as the dual of the identity and use it to compute the number of unipotent elements.
Chapter 5 “Disillusionment and Mobility (1983–2001)” argues that rational-legal administration did not exhaust the list of mezzo or organizational outcomes that resulted from RJ’s institutionalization. RJ’s rational-legal administration encountered six limitations that exposed and exacerbated the organization’s preexisting deficiencies, the IRI’s structural shortcomings, the shah’s neo-patrimonial legacies, and bureaucracy’s inherent flaws. These limitations included heightened centralization, intensified careerism, parliamentary entanglements, emerging corporatization, persistent redundancies, and dual executives. On a micro or individual level, these limitations and the inefficiency and stagnancy that they created caused some former RJ members to experience fatigue, apathy, and disillusionment. At the same time, RJ’s bureaucratization enabled other former members, particularly those who had lobbied for the organization to become a ministry, to experience political and social mobility as government officials, civil servants, and corporate executives – the very individuals whom former RJ members had initially despised as revolutionary activists in light of their anti-bureaucratic and anti-materialistic worldview.
The bridging concept between the abstract and geometric is the theory of realizations. This chapter concentrates on symmetric sets, namely, finite sets on which a group of permutations acts transitively. After a discussion of their basic properties, the concept of their realizations is introduced, with operations on them (such as blending) showing that the family of their congruences classes has the structure of a convex cone. A key idea is that of the inner product and cosine vectors of realizations, which define them up to congruence. The theory up to this point is then illustrated by some examples. It is next shown that, corresponding to the tensor product of representations, there is a product of realizations. Another fundamental notion is that of orthogonality relations for cosine vectors. The different realizations derived from an irreducible representation of the abstract group may form a subcone of the realization cone that is more than 1-dimensional. These are looked at more closely, leading to a definition of cosine matrices for the general realization domain. There follows a discussion of cuts and their relationship with duality. Cosine vectors may have entries in some subfield of the real numbers, with implications for the corresponding realizations. The chapter ends with a brief account of how representations of groups are related to realizations.
Ruitenburg’s Theorem says that every endomorphism f of a finitely generated free Heyting algebra is ultimately periodic if f fixes all the generators but one. More precisely, there is N ≥ 0 such that fN+2 = fN, thus the period equals 2. We give a semantic proof of this theorem, using duality techniques and bounded bisimulation ranks. By the same techniques, we tackle investigation of arbitrary endomorphisms of free algebras. We show that they are not, in general, ultimately periodic. Yet, when they are (e.g. in the case of locally finite subvarieties), the period can be explicitly bounded as function of the cardinality of the set of generators.
We study the derived category of a complete intersection
of bilinear divisors in the orbifold
. Our results are in the spirit of Kuznetsov’s theory of homological projective duality, and we describe a homological projective duality relation between
and a category of modules over a sheaf of Clifford algebras on
. The proof follows a recently developed strategy combining variation of geometric invariant theory (VGIT) stability and categories of global matrix factorisations. We begin by translating
into a derived category of factorisations on a Landau–Ginzburg (LG) model, and then apply VGIT to obtain a birational LG model. Finally, we interpret the derived factorisation category of the new LG model as a Clifford module category. In some cases we can compute this Clifford module category as the derived category of a variety. As a corollary we get a new proof of a result of Hosono and Takagi, which says that a certain pair of non-birational Calabi–Yau 3-folds have equivalent derived categories.
Innovation contributes to a firm's long-term competitive advantages but also involves significant risk and uncertainty. As agency theory predicts, CEOs are self-interested and risk-averse, and thus are reluctant to engage in innovation investments. However, the extent to which CEOs are self-interested and the mechanisms through which self-interested CEOs affect firm innovation have not been empirically tested. To fill this gap, we propose that CEOs possess a mix of both self-preserving and other-regarding motives, and build a mediation model in which CEO values affect firm innovation via firms’ long-term orientation. Based on a three-phase (from 2014 to 2016) survey of 436 Chinese manufacturing firms, we find that CEOs with high self-regarding values reduce innovation efforts and performance by damaging a firm's long-term orientation. Moreover, CEO tenure, CEO duality, and environmental uncertainty weaken the relationship between CEO values and firm innovation via long-term orientation. Our study enriches the innovation literature by extending the basic assumptions of agency theory and by providing empirical evidence to determine whether and how self-regarded CEOs affect firm innovation.
The focus of this chapter is on balanced NC dualizing complexes (DC). Let A be a noetherian connected NC graded ring over the base field K, with enveloping ring Aen = A ⊗K Aop. A complex R ∈ D(Aen,gr) is called a graded NC DC if its cohomology is bounded and finite both sides; it has finite graded injective dimension on both sides; and it has NC derived Morita property (see abstract of Chapter 13) on both sides. A balanced NC DC over A is a pair (R,β), where R is a graded NC DC over A with symmetric derived m-torsion, and β : RΓm(R) → A* is an isomorphism in D(Aen,gr). A balanced DC (R,β) is unique up to a unique isomorphism, and it satisfies the NC Graded Local Duality Theorem. We prove that A has a balanced DC iff A satisfies the χ condition and has finite local cohomological dimension. If A is an Artin--Schelter (AS) regular graded ring, then it has a balanced DC R = A(φ,-l)[n], a twist of the bimodule A by an automorphism φ and integers -l and n.
Let A be a NC noetherian ring, with enveloping ring Aen. A NC DC over A is a complex R ∈ D(Aen) satisfying the conditions stated earlier. The NC square of R is a complex Sq(R) ∈ D(Aen). A NC rigid DC over A is a pair (R,ρ), where R is a NC DC and ρ : R → Sq(R) is an isomorphism in D(Aen). We prove that a rigid NC DC (R,ρ) is unique up to a unique rigid isomorphism. If the ring A admits a filtration such that the graded ring Gr(A) is noetherian connected and has a balanced DC, then A has a rigid DC. This material is due to Van den Bergh. If the graded ring Gr(A) is AS regular, then the rigid NC DC of A is R = A(μ)[n], where μ is a ring automorphism of A and n is an integer. The automorphism ν := μ−1 is called the Nakayama automorphism of A. Such a ring A is called an n-dimensional twisted Calabi--Yau ring. We state and prove the Van den Bergh Duality Theorem for Hochschild (co)homology and give an example of a Calabi--Yau category of fractional dimension.
Official revenue collections in French Indochina were low compared with most other colonies in East and Southeast Asia. This fact stands in contrast to a large body of literature that claims French tax demands were a crushing burden on many indigenous people. French Indochina is often put forward as an example of one of the most extractive colonial states in Asia. This chapter reconciles these seemingly opposing interpretations by examining the formation of the colonial fiscal state, its capacity, and the potential impact on the local population. We argue that the French colonial administration is best characterized as complex, bureaucratic, and centralized. Its fiscal capacity was heavily dependant on the expansion and growth of commercial activities. This led to significant geographical asymmetries in wealth generation and investments, and a complex system of budgetary transfers amongst the different levels of administration. French rule was, however, indirect and responded to local differences. Pre-colonial fiscal institutions survived under French colonial rule, but were not adequately recognised in the figures. This reinforces the claim that the burden to the majority of the population was greater than officially recorded, but it was unevenly distributed.
Chapter 1, ‘Medieval Ovids’, opens the discussion with perhaps the most prolific and the most devious author of autofiction in ancient literature: the poet Ovid. Ovid had no surviving ancient tradition of Lives, but his texts themselves provided an ideal ground for the creation of biofictional narratives. Encoding within them a life-story that deliberately teeters between fiction and reality, Ovid’s texts invited a life-centred reception that illustrates some of the essential dynamics of biofictional reading. With no ancient Life available to them, medieval writers willingly took up Ovid’s implicit invitation to produce biofictional supplements to his texts, telling and retelling stories about the poet’s imaginary lives: from the accessus or ‘introduction’ that typically prefaced texts of ancient authors, often inscribed as a paratext to the poet’s works in the manuscripts themselves, to the thirteenth-century pseudepigraphal De vetula, a 2400-line poem presented as Ovid’s autobiography from exile discovered in the poet’s recently excavated tomb. Seemingly situated on the margins of medieval culture, these experiments in life-writing show that biofictional engagement with Ovid functioned as a dynamic and creative site of reading texts and writing Lives in the period, foregrounding the case for biofiction as a mode of textual engagement in reception.
We find explicit estimates for the exponential rate of long-term convergence for the ruin probability in a level-dependent Lévy-driven risk model, as time goes to infinity. Siegmund duality allows us to reduce the problem to long-term convergence of a reflected jump-diffusion to its stationary distribution, which is handled via Lyapunov functions.
Chapter 7 interrogates the intersection between the global and local when considering options available for an exit from sex work and looks specifically at the role of the state, the NGO sector and grass-roots sex worker activism to show women’s limited space for agency in this process. This chapter explores how gender operates in this context of the negotiated duality of the African state to show that despite the Kenyan state’s efforts to avoid engaging with gender issues more profoundly and a continuous exclusion of women from the remit of the state, it must open some political space for movements with a gender agenda because of its accountability to donors that are driven by liberal ideas of inclusion. The first and the third parts of this chapter illustrate this process t+G11hrough examining sex workers’ narratives regarding the Kenyan state and politics, as well as analysing the politics of the sex worker movement. The second part of the chapter focuses on the engagement with the international sphere, which has important re-gendering or gender-strategic consequences. The limits of the NGO sector to address gendered inequalities and create viable alternatives for people selling sex are interrogated by analysing programmes targeting individuals selling sex.
The variety of Brouwerian semilattices is amalgamable and locally finite; hence, by well-known results , it has a model completion (whose models are the existentially closed structures). In this article, we supply a finite and rather simple axiomatization of the model completion.
We explore the constraints imposed by Poincaré duality on the resonance varieties of a graded algebra. For a three-dimensional Poincaré duality algebra A, we obtain a fairly precise geometric description of the resonance varieties
We introduce a notion of Koszul A∞-algebra that generalizes Priddy's notion of a Koszul algebra and we use it to construct small A∞-algebra models for Hochschild cochains. As an application, this yields new techniques for computing free loop space homology algebras of manifolds that are either formal or coformal (over a field or over the integers). We illustrate these techniques in two examples.
We formulate a theory of pointed manifolds, accommodating both embeddings and Pontryagin–Thom collapse maps, so as to present a common generalization of Poincaré duality in topology and Koszul duality in
The third chapter explores the connections of fluid dynamics with various microscopic approaches and techniques, discussing kinetic theory, gauge/gravity duality, thermal quantum field theory, and lattice field theory.