2,157 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
Effect of magnesium doping on the orbital and magnetic order in LiNiO2
In LiNiO2, the Ni3+ ions, with S=1/2 and twofold orbital degeneracy, are
arranged on a trian- gular lattice. Using muon spin relaxation (MuSR) and
electron spin resonance (ESR), we show that magnesium doping does not stabilize
any magnetic or orbital order, despite the absence of interplane Ni2+. A
disordered, slowly fluctuating state develops below 12 K. In addition, we find
that magnons are excited on the time scale of the ESR experiment. At the same
time, a g factor anisotropy is observed, in agreement with
orbital occupancy
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
Adiabatic Elimination in a Lambda System
This paper deals with different ways to extract the effective two-dimensional
lower level dynamics of a lambda system excited by off-resonant laser beams. We
present a commonly used procedure for elimination of the upper level, and we
show that it may lead to ambiguous results. To overcome this problem and better
understand the applicability conditions of this scheme, we review two rigorous
methods which allow us both to derive an unambiguous effective two-level
Hamiltonian of the system and to quantify the accuracy of the approximation
achieved: the first one relies on the exact solution of the Schrodinger
equation, while the second one resorts to the Green's function formalism and
the Feshbach projection operator technique.Comment: 14 pages, 3 figure
Schubert calculus of Richardson varieties stable under spherical Levi subgroups
We observe that the expansion in the basis of Schubert cycles for
of the class of a Richardson variety stable under a spherical Levi subgroup is
described by a theorem of Brion. Using this observation, along with a
combinatorial model of the poset of certain symmetric subgroup orbit closures,
we give positive combinatorial descriptions of certain Schubert structure
constants on the full flag variety in type . Namely, we describe
when and are inverse to Grassmannian permutations with unique descents
at and , respectively. We offer some conjectures for similar rules in
types and , associated to Richardson varieties stable under spherical
Levi subgroups of SO(2n+1,\C) and SO(2n,\C), respectively.Comment: Section 4 significantly shortened, and other minor changes made as
suggested by referees. Final version, to appear in Journal of Algebraic
Combinatoric
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