5,805 research outputs found
Linear semigroups with coarsely dense orbits
Let be a finitely generated abelian semigroup of invertible linear
operators on a finite dimensional real or complex vector space . We show
that every coarsely dense orbit of is actually dense in . More
generally, if the orbit contains a coarsely dense subset of some open cone
in then the closure of the orbit contains the closure of . In the
complex case the orbit is then actually dense in . For the real case we give
precise information about the possible cases for the closure of the orbit.Comment: We added comments and remarks at various places. 14 page
Another look at anomalous J/Psi suppression in Pb+Pb collisions at P/A = 158 GeV/c
A new data presentation is proposed to consider anomalous
suppression in Pb + Pb collisions at GeV/c. If the inclusive
differential cross section with respect to a centrality variable is available,
one can plot the yield of J/Psi events per Pb-Pb collision as a function of an
estimated squared impact parameter. Both quantities are raw experimental data
and have a clear physical meaning. As compared to the usual J/Psi over
Drell-Yan ratio, there is a huge gain in statistical accuracy. This
presentation could be applied advantageously to many processes in the field of
nucleus-nucleus collisions at various energies.Comment: 6 pages, 5 figures, submitted to The European Physical Journal C;
minor revisions for final versio
On the bounded cohomology of semi-simple groups, S-arithmetic groups and products
We prove vanishing results for Lie groups and algebraic groups (over any
local field) in bounded cohomology. The main result is a vanishing below twice
the rank for semi-simple groups. Related rigidity results are established for
S-arithmetic groups and groups over global fields. We also establish vanishing
and cohomological rigidity results for products of general locally compact
groups and their lattices
Hodge structures associated to SU(p,1)
Let A be an abelian variety over C such that the semisimple part of the Hodge
group of A is a product of copies of SU(p,1) for some p>1. We show that any
effective Tate twist of a Hodge structure occurring in the cohomology of A is
isomorphic to a Hodge structure in the cohomology of some abelian variety
A Note on the Equality of Algebraic and Geometric D-Brane Charges in WZW Models
The algebraic definition of charges for symmetry-preserving D-branes in
Wess-Zumino-Witten models is shown to coincide with the geometric definition,
for all simple Lie groups. The charge group for such branes is computed from
the ambiguities inherent in the geometric definition.Comment: 12 pages, fixed typos, added references and a couple of remark
Fomenko-Mischenko Theory, Hessenberg Varieties, and Polarizations
The symmetric algebra g (denoted S(\g)) over a Lie algebra \g (frak g) has
the structure of a Poisson algebra. Assume \g is complex semi-simple. Then
results of Fomenko- Mischenko (translation of invariants) and A.Tarasev
construct a polynomial subalgebra \cal H = \bf C[q_1,...,q_b] of S(\g) which is
maximally Poisson commutative. Here b is the dimension of a Borel subalgebra of
\g. Let G be the adjoint group of \g and let \ell = rank \g. Identify \g with
its dual so that any G-orbit O in \g has the structure (KKS) of a symplectic
manifold and S(\g) can be identified with the affine algebra of \g. An element
x \in \g is strongly regular if \{(dq_i)_x\}, i=1,...,b, are linearly
independent. Then the set \g^{sreg} of all strongly regular elements is Zariski
open and dense in \g, and also \g^{sreg \subset \g^{reg} where \g^{reg} is the
set of all regular elements in \g. A Hessenberg variety is the b-dimensional
affine plane in \g, obtained by translating a Borel subalgebra by a suitable
principal nilpotent element. This variety was introduced in [K2]. Defining Hess
to be a particular Hessenberg variety, Tarasev has shown that Hess \subset
\g^sreg. Let R be the set of all regular G-orbits in \g. Thus if O \in R, then
O is a symplectic manifold of dim 2n where n= b-\ell. For any O\in R let
O^{sreg} = \g^{sreg}\cap O. We show that O^{sreg} is Zariski open and dense in
O so that O^{sreg} is again a symplectic manifold of dim 2n. For any O \in R
let Hess (O) = Hess \cap O. We prove that Hess(O) is a Lagrangian submanifold
of O^{sreg} and Hess =\sqcup_{O \in R} Hess(O). The main result here shows that
there exists, simultaneously over all O \in R, an explicit polarization (i.e.,
a "fibration" by Lagrangian submanifolds) of O^{sreg} which makes O^{sreg}
simulate, in some sense, the cotangent bundle of Hess(O).Comment: 36 pages, plain te
-Spectral theory of locally symmetric spaces with -rank one
We study the -spectrum of the Laplace-Beltrami operator on certain
complete locally symmetric spaces with finite volume and
arithmetic fundamental group whose universal covering is a
symmetric space of non-compact type. We also show, how the obtained results for
locally symmetric spaces can be generalized to manifolds with cusps of rank
one
Arithmeticity vs. non-linearity for irreducible lattices
We establish an arithmeticity vs. non-linearity alternative for irreducible
lattices in suitable product groups, such as for instance products of
topologically simple groups. This applies notably to a (large class of)
Kac-Moody groups. The alternative relies on a CAT(0) superrigidity theorem, as
we follow Margulis' reduction of arithmeticity to superrigidity.Comment: 11 page
The congruence kernel of an arithmetic lattice in a rank one algebraic group over a local field
Let k be a global field and let k_v be the completion of k with respect to v,
a non-archimedean place of k. Let \mathbf{G} be a connected, simply-connected
algebraic group over k, which is absolutely almost simple of k_v-rank 1. Let
G=\mathbf{G}(k_v). Let \Gamma be an arithmetic lattice in G and let C=C(\Gamma)
be its congruence kernel. Lubotzky has shown that C is infinite, confirming an
earlier conjecture of Serre. Here we provide complete solution of the
congruence subgroup problem for \Gamm$ by determining the structure of C. It is
shown that C is a free profinite product, one of whose factors is
\hat{F}_{\omega}, the free profinite group on countably many generators. The
most surprising conclusion from our results is that the structure of C depends
only on the characteristic of k. The structure of C is already known for a
number of special cases. Perhaps the most important of these is the
(non-uniform) example \Gamma=SL_2(\mathcal{O}(S)), where \mathcal{O}(S) is the
ring of S-integers in k, with S=\{v\}, which plays a central role in the theory
of Drinfeld modules. The proof makes use of a decomposition theorem of
Lubotzky, arising from the action of \Gamma on the Bruhat-Tits tree associated
with G.Comment: 27 pages, 5 figures, to appear in J. Reine Angew. Mat
Multiplets of free d- and f-metal ions: A systematic DFT study
In this work we apply in a systematic way our multi-determinantal model to calculate the fine structure of the whole atomic multiplet manifold. The key feature of this approach is the explicit treatment of near-degeneracy correlation using ad hoc configuration interaction (CI) within the active space of KohnâSham (KS) orbitals with open d- or f-shells. The calculation of the CI-matrices is based on a central symmetry decomposition of the energies of all single determinants (micro-states) calculated according to Density Functional Theory (DFT) for frozen KS-orbitals corresponding to the averaged configuration, eventually with fractional occupations, of the d- or f-orbitals and/or the direct calculation of the electrostatic reduced matrix elements (Racah or SlaterâCondon parameters) occurring in the corresponding active space. We performed DFT calculations on all divalent and trivalent dÂČâdâž metal ions, as well as the fÂČâfÂčÂČ lanthanide(III) ions. We compare the results of both variants of the method with the data available in the literature. Both procedures yield multiplet energies with an accuracy of about hundred wave numbers and fine structure splitting accurate to less than a tenth of this amount
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