Cuspidal representations of rational Cherednik algebras at t=0

We study those finite dimensional quotients of the rational Cherednik algebra at t=0 that are supported at a point of the centre. It is shown that each such quotient is Morita equivalent to a certain cuspidal quotient of a rational Cherednik algebra associated to a parabolic subgroup of W

Counting resolutions of symplectic quotient singularities

Let $\Gamma$ be a finite subgroup of $\mathrm{Sp}(V)$. In this article we count the number of symplectic resolutions admitted by the quotient singularity $V / \Gamma$. Our approach is to compare the universal Poisson deformation of the symplectic quotient singularity with the deformation given by the Calogero-Moser space. In this way, we give a simple formula for the number of $\mathbb{Q}$-factorial terminalizations admitted by the symplectic quotient singularity in terms of the dimension of a certain Orlik-Solomon algebra naturally associated to the Calogero-Moser deformation. This dimension is explicitly calculated for all groups $\Gamma$ for which it is known that $V / \Gamma$ admits a symplectic resolution. As a consequence of our results, we confirm a conjecture of Ginzburg and Kaledin.Comment: 13 pages, final versio

Four models of European citizenship

This paper identifies two ideal types of citizenship - the cosmopolitan and the communitarian, that correspond to the transnational and sub/national levels of the European Union respectively, and examines four different ways in which they might be combined

Which constitution for what kind of Europe?

Discussion of the pros and cons of an EU constitution tends to focus upon two issues. On the one hand, proponents and opponents of reform seek to legitimate the EU as a 'regime', or form of governance. For example, strengthening the powers of the European Parliament is hoped to improve democratic accountability, while incorporating the Charter of Fundamental Rights of the EU is suggested as a way of enhancing legal integrity and the rule of law. On the other hand, debate centres on the EU's status as a 'polity', and the degree to which a Constitution might allow a clear demarcation of what is the EU's area of competence and what remains the domain of domestic governments and legal systems. These two issues are inter-related. Yet, neither politicians nor many academics explicitly address the connections between them. Some focus on 'regime' considerations and seek, almost as an after thought, to tailor them to their preferred view of the EU polity. Others, especially Eurosceptics, treat the very discussion of the EU as having a regime, as an undesirable move in the direction of acknowledging it as a polity. In this piece I wish to suggest that both approaches are misguided. Regime and polity interact, with the latter constraining (without determining) the former. I shall explore the three dominant models of constitutionalism to be found within European political discourse: a rights-based model, a popular sovereignty model and a common law model that employs elements of each. Whilst the first two are the most frequently employed by proponents of constitutional reform, I shall suggest that it is the third that best represents the actually existing EU constitution. Moreover, it has been the key to the successful integration of Europe hitherto precisely because it has allowed both the 'regime', and 'polity', dimensions of the EU to develop in tandem

On singular Calogero-Moser spaces

Using combinatorial properties of complex reflection groups, we show that the generalised Calogero-Moser space associated to the centre of the corresponding rational Cherednik algebra is singular for all values of its deformation parameter c if and only if the group is different from the wreath product $S_n\wr C_m$ and the binary tetrahedral group. This result and a theorem of Ginzburg and Kaledin imply that there does not exist a symplectic resolution of the singular symplectic variety h+h*/W outside of these cases; conversely we show that there exists a symplectic resolution for the binary tetrahedral group (Hilbert schemes provide resolutions for the wreath product case).Comment: Conjecture 1.3 of version 1 is proved as Corollary 4.2. Inconsistent use of notation in the proof of Lemma 3.3 corrected (thanks to Ulrich Thiel for pointing this out

The democratic legitimacy of international human rights conventions: Political constitutionalism and the European convention on human rights

International Human Rights Courts (IHRCts), such as the European Court of Human Rights (ECtHR), have come under increasing criticism as being incompatible with domestic judicial and legislative mechanisms for upholding rights. These domestic instruments are said to possess greater democratic legitimacy than international instruments do or could do. Within the UK this critique has led some prominent judges and politicians to propose withdrawing from the European Convention on Human Rights (ECHR). Legal cosmopolitans respond by denying the validity of this democratic critique. By contrast this article argues that such criticisms are defensible from a political constitutionalist perspective but that International Human Rights Conventions (IHRCs) can nevertheless be understood in ways that meet them. To do so, IHRC must be conceived as legislated for and controlled by an international association of democratic states, which authorizes IHRCts and holds them accountable, limiting them to 'weak review'. The resulting model of IHRC is that of a 'two level' political constitution. The ECHR is shown to largely accord with this model, which is argued to be both more plausible and desirable than a legal cosmopolitan model that sidelines democracy and advocates 'strong' review

The liberty of the post-moderns? Market and civic freedom within the EU

Taking its cue from Benjamin's Constant's famous essay, this article uses the case of EU citizenship to explore how far ancient, civic, freedom can be combined with modern, market, freedom. Many commentators have, in different ways, argued that the forces promoting European integration call for a new form of post-national citizenship that either builds civic freedom on the basis of the liberties of the moderns or does away with the need for it altogether. These arguments are disputed. Constant perceptively raised a number of problems with this analysis, while ignoring - or being ignorant of - a number of others. As he noted, ancient liberty corrects various pathologies and lacunas of modern liberty, but he overlooked the degree to which its survival rested on the continuing importance of certain pre-modern forms of social solidarity in modern times. Those seeking new forms of post-modern citizenship tend to ignore one or other or both these points. The piece concludes by arguing that the only practical way of combining ancient and modern liberty within the EU is to view it as a particularly intense form of international cooperation between democratic states rather than as a supranational organisation that transcends its component parts