1,662 research outputs found
Spherical orbit closures in simple projective spaces and their normalizations
Let G be a simply connected semisimple algebraic group over an algebraically
closed field k of characteristic 0 and let V be a rational simple G-module of
finite dimension. If G/H \subset P(V) is a spherical orbit and if X is its
closure, then we describe the orbits of X and those of its normalization. If
moreover the wonderful completion of G/H is strict, then we give necessary and
sufficient combinatorial conditions so that the normalization morphism is a
homeomorphism. Such conditions are trivially fulfilled if G is simply laced or
if H is a symmetric subgroup.Comment: 24 pages, LaTeX. v4: Final version, to appear in Transformation
Groups. Simplified some proofs and corrected minor mistakes, added
references. v3: major changes due to a mistake in previous version
A combinatorial smoothness criterion for spherical varieties
We suggest a combinatorial criterion for the smoothness of an arbitrary
spherical variety using the classification of multiplicity-free spaces,
generalizing an earlier result of Camus for spherical varieties of type .Comment: 14 pages, 2 table
Classification of Reductive Monoid Spaces Over an Arbitrary Field
In this semi-expository paper we review the notion of a spherical space. In
particular we present some recent results of Wedhorn on the classification of
spherical spaces over arbitrary fields. As an application, we introduce and
classify reductive monoid spaces over an arbitrary field.Comment: This is the final versio
K-orbit closures on G/B as universal degeneracy loci for flagged vector bundles with symmetric or skew-symmetric bilinear form
We use equivariant localization and divided difference operators to determine
formulas for the torus-equivariant fundamental cohomology classes of -orbit
closures on the flag variety , where G = GL(n,\C), and where is one
of the symmetric subgroups O(n,\C) or Sp(n,\C). We realize these orbit
closures as universal degeneracy loci for a vector bundle over a variety
equipped with a single flag of subbundles and a nondegenerate symmetric or
skew-symmetric bilinear form taking values in the trivial bundle. We describe
how our equivariant formulas can be interpreted as giving formulas for the
classes of such loci in terms of the Chern classes of the various bundles.Comment: Minor revisions and corrections suggested by referees. Final version,
to appear in Transformation Group
Non-Holonomic Control IV : Coherence Protection in a Rubidium isotope
In this paper, we present a realistic application of the coherence protection
method proposed in the previous article. A qubit of information encoded on the
two spin states of a Rubidium isotope is protected from the action of electric
and magnetic fields
Non-Holonomic Control I
In this paper, we present a universal control technique, the non-holonomic
control, which allows us to impose any arbitrarily prescribed unitary evolution
to any quantum system through the alternate application of two well-chosen
perturbations
GALEX J201337.6+092801: The lowest gravity subdwarf B pulsator
We present the recent discovery of a new subdwarf B variable (sdBV), with an
exceptionally low surface gravity. Our spectroscopy of J20136+0928 places it at
Teff = 32100 +/- 500, log(g) = 5.15 +/- 0.10, and log(He/H) = -2.8 +/- 0.1.
With a magnitude of B = 12.0, it is the second brightest V361 Hya star ever
found. Photometry from three different observatories reveals a temporal
spectrum with eleven clearly detected periods in the range 376 to 566 s, and at
least five more close to our detection limit. These periods are unusually long
for the V361 Hya class of short-period sdBV pulsators, but not unreasonable for
p- and g-modes close to the radial fundamental, given its low surface gravity.
Of the ~50 short period sdB pulsators known to date, only a single one has been
found to have comparable spectroscopic parameters to J20136+0928. This is the
enigmatic high-amplitude pulsator V338 Ser, and we conclude that J20136+0928 is
the second example of this rare subclass of sdB pulsators located well above
the canonical extreme horizontal branch in the HR diagram.Comment: 5 pages, accepted for publication in ApJ Letter
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