1,856 research outputs found
Andersen Filtration and Hard Lefschetz
On the space of homomorphisms from a Verma module to an indecomposable
tilting module of the BGG-category O we define a natural filtration following
Andersen and establish a formula expressing the dimensions of the filtration
steps in terms of coefficients of Kazhdan-Lusztig polynomials.Comment: English version of math.RT/0604589, v3 revised translatio
Quantitative measurement of the surface charge density
We present a method of measuring the charge density on dielectric surfaces.
Similar to electrostatic force microscopy we record the electrostatic
interaction between the probe and the sample surface, but at large tip-sample
distances. For calibration we use a pyroelectric sample which allows us to
alter the surface charge density by a known amount via a controlled temperature
change. For proof of principle we determined the surface charge density under
ambient conditions of ferroelectric lithium niobate
Parabolic category O, perverse sheaves on Grassmannians, Springer fibres and Khovanov homology
For a fixed parabolic subalgebra p of gl(n,C) we prove that the centre of the
principal block O(p) of the parabolic category O is naturally isomorphic to the
cohomology ring of the corresponding Springer fibre. We give a diagrammatic
description of O(p) for maximal parabolic p and give an explicit isomorphism to
Braden's description of the category Perv_B(G(n,n)) of perverse sheaves on
Grassmannians. As a consequence Khovanov's algebra H^n is realised as the
endomorphism ring of some object from Perv_B(G(n,n)) which corresponds under
localisation and the Riemann-Hilbert correspondence to a full
projective-injective module in the corresponding category . From there
one can deduce that Khovanov's tangle invariants are obtained from the more
general functorial invariants involving category O by restriction.Comment: 39 pages, 9 figures, added a few remark
Khovanov-Rozansky homology via a canopolis formalism
In this paper, we describe a canopolis (i.e. categorified planar algebra)
formalism for Khovanov and Rozansky's link homology theory. We show how this
allows us to organize simplifications in the matrix factorizations appearing in
their theory. In particular, it will put the equivalence of the original
definition of Khovanov-Rozansky homology and the definition using Soergel
bimodules in a more general context, allow us to give a new proof of the
invariance of triply graded homology and give new analysis of the behavior of
triply graded homology under the Reidemeister IIb move.Comment: 24 pages, 7 figures. v3: edited introduction and fixed diagram 1,
plus minor change
Quantitative analysis of ferroelectric domain imaging with piezoresponse force microscopy
The contrast mechanism for ferroelectric domain imaging via piezoresponse
force microscopy (PFM) is investigated. A novel analysis of PFM measurements is
presented which takes into account the background caused by the experimental
setup. This allows, for the first time, a quantitative, frequency independent
analysis of the domain contrast which is in good agreement with the expected
values for the piezoelectric deformation of the sample and satisfies the
generally required features of PFM imaging
Modular Koszul duality
We prove an analogue of Koszul duality for category of a
reductive group in positive characteristic larger than 1 plus the
number of roots of . However there are no Koszul rings, and we do not prove
an analogue of the Kazhdan--Lusztig conjectures in this context. The main
technical result is the formality of the dg-algebra of extensions of parity
sheaves on the flag variety if the characteristic of the coefficients is at
least the number of roots of plus 2.Comment: 62 pages; image displays best in pd
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