1,960 research outputs found
Irreducible characters of GSp(4, q) and dimensions of spaces of fixed vectors
In this paper, we compute the conjugacy classes and the list of irreducible
characters of GSp(4,q), where q is odd. We also determine precisely which
irreducible characters are non-cuspidal and which are generic. These characters
are then used to compute dimensions of certain subspaces of fixed vectors of
smooth admissible non-supercuspidal representations of GSp(4,F), where F is a
non-archimedean local field of characteristic zero with residue field of order
q.Comment: 48 pages, 21 tables. Corrected an error in Table 16 for type V*
representations (theta_11 and theta_12 were switched
Diacetato[N,N′-bis(2-pyridylmethylidene)cyclohexane-1,2-diamine]manganese(II) hexahydrate
The asymmetric unit of the title compound, [Mn(C2H3O2)2(C18H20N4)]·6H2O, consists of a neutral MnII complex with six solvent water molecules. In the complex, the Mn2+ ion is eight-coordinated in a distorted square-antiprismatic environment by four N atoms from the tetradentate ligand N,N′-bis(2-pyridylmethylidene)cyclohexane-1,2-diamine (bpic) and four O atoms from two acetate ligands. The compound displays intermolecular O—H⋯O hydrogen-bond interactions to form various kinds of ring structures and cyclic water clusters
Manifestly Supersymmetric RG Flows
Renormalisation group (RG) equations in two-dimensional N=1 supersymmetric
field theories with boundary are studied. It is explained how a manifestly N=1
supersymmetric scheme can be chosen, and within this scheme the RG equations
are determined to next-to-leading order. We also use these results to revisit
the question of how brane obstructions and lines of marginal stability appear
from a world-sheet perspective.Comment: 22 pages; references added, minor change
Categorification of a linear algebra identity and factorization of Serre functors
We provide a categorical interpretation of a well-known identity from linear
algebra as an isomorphism of certain functors between triangulated categories
arising from finite dimensional algebras.
As a consequence, we deduce that the Serre functor of a finite dimensional
triangular algebra A has always a lift, up to shift, to a product of suitably
defined reflection functors in the category of perfect complexes over the
trivial extension algebra of A.Comment: 18 pages; Minor changes, references added, new Section 2.
Semi-invariants of symmetric quivers of finite type
Let be a symmetric quiver, where is a finite
quiver without oriented cycles and is a contravariant involution on
. The involution allows us to define a nondegenerate bilinear
form on a representation $V$ of $Q$. We shall call the representation
orthogonal if is symmetric and symplectic if is skew-symmetric.
Moreover we can define an action of products of classical groups on the space
of orthogonal representations and on the space of symplectic representations.
For symmetric quivers of finite type, we prove that the rings of
semi-invariants for this action are spanned by the semi-invariants of
determinantal type and, in the case when matrix defining is
skew-symmetric, by the Pfaffians
Homological algebra for osp(1/2n)
We discuss several topics of homological algebra for the Lie superalgebra
osp(1|2n). First we focus on Bott-Kostant cohomology, which yields classical
results although the cohomology is not given by the kernel of the Kostant
quabla operator. Based on this cohomology we can derive strong
Bernstein-Gelfand-Gelfand resolutions for finite dimensional osp(1|2n)-modules.
Then we state the Bott-Borel-Weil theorem which follows immediately from the
Bott-Kostant cohomology by using the Peter-Weyl theorem for osp(1|2n). Finally
we calculate the projective dimension of irreducible and Verma modules in the
category O
Semi-invariants of symmetric quivers of tame type
A symmetric quiver is a finite quiver without oriented cycles
equipped with a contravariant involution on . The involution allows us to define a nondegenerate bilinear form on
a representation $V$ of $Q$. We shall say that $V$ is orthogonal if is
symmetric and symplectic if is skew-symmetric. Moreover, we define an
action of products of classical groups on the space of orthogonal
representations and on the space of symplectic representations. So we prove
that if is a symmetric quiver of tame type then the rings of
semi-invariants for this action are spanned by the semi-invariants of
determinantal type and, when matrix defining is skew-symmetric, by
the Pfaffians . To prove it, moreover, we describe the symplectic and
orthogonal generic decomposition of a symmetric dimension vector
The return of the bursts: Thermonuclear flashes from Circinus X-1
We report the detection of 15 X-ray bursts with RXTE and Swift observations
of the peculiar X-ray binary Circinus X-1 during its May 2010 X-ray
re-brightening. These are the first X-ray bursts observed from the source after
the initial discovery by Tennant and collaborators, twenty-five years ago. By
studying their spectral evolution, we firmly identify nine of the bursts as
type I (thermonuclear) X-ray bursts. We obtain an arcsecond location of the
bursts that confirms once and for all the identification of Cir X-1 as a type I
X-ray burst source, and therefore as a low magnetic field accreting neutron
star. The first five bursts observed by RXTE are weak and show approximately
symmetric light curves, without detectable signs of cooling along the burst
decay. We discuss their possible nature. Finally, we explore a scenario to
explain why Cir X-1 shows thermonuclear bursts now but not in the past, when it
was extensively observed and accreting at a similar rate.Comment: Accepted for publication in The Astrophysical Journal Letters. Tables
1 & 2 merged. Minor changes after referee's comments. 5 pages, 4 Figure
On Arnold's 14 `exceptional' N=2 superconformal gauge theories
We study the four-dimensional superconformal N=2 gauge theories engineered by
the Type IIB superstring on Arnold's 14 exceptional unimodal singularities
(a.k.a. Arnold's strange duality list), thus extending the methods of 1006.3435
to singularities which are not the direct sum of minimal ones. In particular,
we compute their BPS spectra in several `strongly coupled' chambers.
From the TBA side, we construct ten new periodic Y-systems, providing
additional evidence for the existence of a periodic Y-system for each isolated
quasi-homogeneous singularity with (more generally, for each N=2
superconformal theory with a finite BPS chamber whose chiral primaries have
dimensions of the form N/l).Comment: 73 pages, 7 figure
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