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

A new linear quotient of C⁴ admitting a symplectic resolution

We show that the quotient C^4/G admits a symplectic resolution for G = (Q_8 x D_8)/(Z/2) < Sp(4,C). Here Q_8 is the quaternionic group of order eight and D_8 is the dihedral group of order eight, and G is the quotient of their direct product which identifies the nontrivial central elements -1 of each. It is equipped with the tensor product of the defining two-dimensional representations of Q_8 and D_8. This group is also naturally a subgroup of the wreath product group of Q_8 by S_2. We compute the singular locus of the family of commutative spherical symplectic reflection algebras deforming C^4/G. We also discuss preliminary investigations on the more general question of classifying linear quotients V / G admitting symplectic resolutions

A summary of the published data on host plants and morphology of immature stages of Australian jewel beetles (Coleoptera: Buprestidae) : with additional new records

A summary is given of the published host plant and descriptive immature stage morphology data for 671 species and 11 subspecies in 54 genera of Australian jewel beetles (Coleoptera: Buprestidae). New host data for 155 species and 3 subspecies in 17 genera including the first published data for 75 species are included

Symplectic resolutions of character varieties

In this article we consider the connected component of the identity of $G$-character varieties of compact Riemann surfaces of genus $g > 0$, for connected complex reductive groups $G$ of type $A$ (e.g., $SL_n$ and $GL_n$). We show that these varieties are symplectic singularities and classify which admit symplectic resolutions. The classification reduces to the semi-simple case, where we show that a resolution exists if and only if either $g=1$ and $G$ is a product of special linear groups of any rank and copies of the group $PGL_2$, or if $g=2$ and $G = (SL_2)^m$ for some $m$

Symplectic resolutions of Quiver varieties and character varieties

In this article, we consider Nakajima quiver varieties from the point of view of symplectic algebraic geometry. We prove that they are all symplectic singularities in the sense of Beauville and completely classify which admit symplectic resolutions. Moreover we show that the smooth locus coincides with the locus of theta-canonically polystable points, generalizing a result of Le Bruyn, and we describe the Namikawa Weyl group. An interesting consequence of our results is that not all symplectic resolutions of quiver varieties appear to come from variation of GIT. We apply this to the G-character variety of a compact Riemann surface of genus g > 0, when G is SL(n, C) or GL(n, C). We show that these varieties are symplectic singularities and classify when they admit symplectic resolutions: they do when g = 1 or (g, n) = (2, 2) (assuming n ≥ 2). This is analogous to the case of a quiver with one vertex, g arrows, and dimension vector (n). We note that our results show that existence of proper and projective symplectic resolutions are equivalent for the varieties in question. This does not seem to be known in general

Cryptic diversity of the jewel beetles Agrilus viridis (Coleoptera: Buprestidae) hosted on hazelnut

The genus Agrilus (Coleoptera: Buprestidae) represents a taxonomic puzzle, since the boundaries between species, subspecies and morphotypes tied to different host plants are sometimes difficult to establish on morphological characteristics alone. Some Agrilus species can cause severe agricultural damage; this makes correct distinctions of the taxon and knowing whether the insects switch from one host plant to another important. This study of mtDNA examined the genetic characteristics of lineages of A. viridis, a jewel beetle recently found causing damage to the hazelnut Corylus avellana in NW Italy. Three mitochondrial markers (a portion of the 12S rDNA and a DNA-fragment including partial NADH dehydrogenase subunit I gene, the tRNA Leucine gene and partial 16S rDNA, and partial  Cytochrome c oxidase) were compared between individuals collected on birch Betula sp., beech Fagus sp., willow Salix sp., alder Alnus sp. and hazelnut. We found a high genetic distance between A. viridis sampled on different host plants, while individuals sampled on the same host plant were similar despite a considerable geographic gap between sampled areas. Our study supports the general pattern for strong ecological separation between populations living on different host plants

On symplectic resolutions and factoriality of Hamiltonian reductions

Recently, Herbig–Schwarz–Seaton have shown that 3-large representations of a reductive group G give rise to a large class of symplectic singularities via Hamiltonian reduction. We show that these singularities are always terminal. We show that they are Q -factorial if and only if G has finite abelianization. When G is connected and semi-simple, we show they are actually locally factorial. As a consequence, the symplectic singularities do not admit symplectic resolutions when G is semi-simple. We end with some open questions

Design and construction of new central and forward muon counters for CDF II

New scintillation counters have been designed and constructed for the CDF upgrade in order to complete the muon coverage of the central CDF detector, and to extend this coverage to larger pseudorapidity. A novel light collection technique using wavelength shifting fibers, together with high quality polystyrene-based scintillator resulted in compact counters with good and stable light collection efficiency over lengths extending up to 320 cm. Their design and construction is described and results of their initial performance are reported.Comment: 20 pages, 15 figure