A reduction principle for Fourier coefficients of automorphic forms

In this paper we analyze a general class of Fourier coefficients of automorphic forms on reductive adelic groups $\mathbf{G}(\mathbb{A}_\mathbb{K})$ and their covers. We prove that any such Fourier coefficient is expressible through integrals and sums involving 'Levi-distinguished' Fourier coefficients. By the latter we mean the class of Fourier coefficients obtained by first taking the constant term along the nilradical of a parabolic subgroup, and then further taking a Fourier coefficient corresponding to a $\mathbb{K}$-distinguished nilpotent orbit in the Levi quotient. In a follow-up paper we use this result to establish explicit formulas for Fourier expansions of automorphic forms attached to minimal and next-to-minimal representations of simply-laced reductive groups.Comment: 35 pages. v2: Extended results and paper split into two parts with second part appearing soon. New title to reflect new focus of this part. v3: Minor corrections and updated reference to the second part that has appeared as arXiv:1908.08296. v4: Minor corrections and reformulation

Eulerianity of Fourier coefficients of automorphic forms

We study the question of Eulerianity (factorizability) for Fourier coefficients of automorphic forms, and we prove a general transfer theorem that allows one to deduce the Eulerianity of certain coefficients from that of another coefficient. We also establish a `hidden' invariance property of Fourier coefficients. We apply these results to minimal and next-to-minimal automorphic representations, and deduce Eulerianity for a large class of Fourier and Fourier-Jacobi coefficients. In particular, we prove Eulerianity for parabolic Fourier coefficients with characters of maximal rank for a class of Eisenstein series in minimal and next-to-minimal representations of groups of ADE-type that are of interest in string theory.Comment: 28 pages. v2: Clarified connection to Fourier-Jacobi coefficients and references added. v3: Minor correction

Acromegaly, Mr Punch and caricature.

The origin of Mr Punch from the Italian Pulcinella of the Commedia dell'arte is well known but his feature, large hooked nose, protruding chin, kyphosis and sternal protrusion all in an exaggerated form also suggest the caricature of an acromegalic. This paper looks at the physical characteristics of acromegaly, the origin of Mr Punch and the development of caricature linking them together in the acromegalic caricature that now has a life of its own

Derivatives for smooth representations of GL(n,R) and GL(n,C)

The notion of derivatives for smooth representations of GL(n) in the p-adic case was defined by J. Bernstein and A. Zelevinsky. In the archimedean case, an analog of the highest derivative was defined for irreducible unitary representations by S. Sahi and called the "adduced" representation. In this paper we define derivatives of all order for smooth admissible Frechet representations (of moderate growth). The archimedean case is more problematic than the p-adic case; for example arbitrary derivatives need not be admissible. However, the highest derivative continues being admissible, and for irreducible unitarizable representations coincides with the space of smooth vectors of the adduced representation. In [AGS] we prove exactness of the highest derivative functor, and compute highest derivatives of all monomial representations. We prove exactness of the highest derivative functor, and compute highest derivatives of all monomial representations. We apply those results to finish the computation of adduced representations for all irreducible unitary representations and to prove uniqueness of degenerate Whittaker models for unitary representations, thus completing the results of [Sah89, Sah90, SaSt90, GS12].Comment: First version of this preprint was split into 2. The proofs of two theorems which are technically involved in analytic difficulties were separated into "Twisted homology for the mirabolic nilradical" preprint. All the rest stayed in v2 of this preprint. v3: version to appear in the Israel Journal of Mathematic

Legitimacy gaps, taxpayer conflict, and the politics of austerity in the UK

Following the 2008 financial crisis, fiscal deficit reduction has become the name of the game for many Western states. This article uses focus group data to explore the legitimation of austerity in the United Kingdom. It is argued that fiscal consolidation speaks to real concerns citizens have over unfair redistribution to supposed ‘undeserving’ groups. The undeserving rich and poor are stigmatised during times of austerity since they are assumed to take more than they give from the public purse—leaving taxpayers, the assumption goes, to pick up the bill. By speaking to this legitimacy gap between prudent normative expectations and the lived experiences of state profligacy, fiscal consolidation can appear to speak to the interests of ‘the taxpayer’—a group conceptualised as a sense of group position that arises from collective sense-making rather than a pre-given constituency

Investigating the potentially contradictory microfoundations of financialization

The existing academic literature on financialization points to multiple instances in which firms attempt to demonstrate the vitality of their stock-market position in ways which ultimately prove to be self-harming. I demonstrate, in the first instance as a matt er of immanent logic, that these actions are linked to the interplay of contradictory tendencies in the microfoundations of financialization. Under conditions of financialization, firms create additional sources of credit to capitalize their productive activities by driving their stock price into greater increases than the market average, thereby generating capital gains. Yet, the more it becomes public knowledge that the financing tricks used to inflate the stock price provide no productive benefit to the firm, the more it would seem to create incentives for fund managers to hold portfolios that replicate the stock market as a whole. In this way, they will minimize their exposure to financial misrepresentation. Such a stance undermines financialized business models, but it does in any case conform to fund managers' basic theoretical training, which revolves around the logical demonstration that an individual stock cannot systematically out-perform the market average. I review the available empirical studies of fund manager decision-making to show that they find against the existence of a simple performativity loop operating between finance theory and fund manager behaviour. However, on many points the empirical evidence does confirm the theoretically derived conclusion concerning the potentially contradictory microfoundations of financialization. Fund managers often do act in a way which is consistent with finance theory's core claim that an index-tracking strategy represents the only equilibrium portfolio, even if this is only rarely as a result of the direct performativity of the theory

Republicanism and the political economy of democracy

Europe is experiencing rapidly accelerating poverty and social exclusion, following half a decade of financial crisis and austerity politics. The key problem behind Europe's malaise, in our view, is the economic disenfranchisement of large parts of its population in the winner-takes-all-society. This article proposes that we examine the contribution of republican political theory as a distinctive approach that provides us with the conceptual and normative resources to reclaim what we call the political economy of democracy, the constellation of political and economic institutions aimed at promoting broad economic sovereignty and individuals' capacities to govern their own lives. This article identifies three key ideas that together constitute a distinctively republican approach to political economy: (1) establish an economic floor; (2) impose an economic ceiling to counter excess economic inequality; and (3) democratize the governance and regulation of the main economic institutions

Contested firm governance, institutions and the undertaking of corporate restructuring practices in Germany

This article investigates the undertaking of corporate restructuring practices (employee downsizing and wage moderation) in Germany from 2008 to 2015. The article presents a political perspective that draws on the insights of the power resources approach and of institutional analyses. The theoretical framework highlights how institutional arrangements structure power relations within companies by empowering, in an asymmetrical manner, different categories of firm stakeholders (employees, managers and shareholders) as well as shaping how they relate to each other in an interactive manner. The article’s empirical findings point to the importance of extensive, but contingent, corporate restructuring in Germany. Companies are more likely to implement ‘defensive’ corporate restructuring practices under conditions of high leverage/debt than when confronted by shareholder value driven investors, thereby reflecting the presence of overlapping interests between employees and managers