2,389 research outputs found
Intersection cohomology of Drinfeld's compactifications
Let be a smooth complete curve, be a reductive group and
a parabolic.
Following Drinfeld, one defines a compactification \widetilde{\on{Bun}}_P
of the moduli stack of -bundles on .
The present paper is concerned with the explicit description of the
Intersection Cohomology sheaf of \widetilde{\on{Bun}}_P. The description is
given in terms of the combinatorics of the Langlands dual Lie algebra
.Comment: An erratum adde
Modules over the small quantum group and semi-infinite flag manifold
We develop a theory of perverse sheaves on the semi-infinite flag manifold
, and show that the subcategory of Iwahori-monodromy
perverse sheaves is equivalent to the regular block of the category of
representations of the small quantum group at an even root of unity
Boundedness and Stability of Impulsively Perturbed Systems in a Banach Space
Consider a linear impulsive equation in a Banach space
with . Suppose each solution of
the corresponding semi-homogeneous equation
(2) is bounded for any bounded sequence .
The conditions are determined ensuring
(a) the solution of the corresponding homogeneous equation has an exponential
estimate;
(b) each solution of (1),(2) is bounded on the half-line for any bounded
and bounded sequence ;
(c) for any tending to
zero;
(d) exponential estimate of implies a similar estimate for .Comment: 19 pages, LaTex-fil
Recommended from our members
Intersection cohomology of Drinfeld‚s compactifications
Let X be a smooth complete curve, G be a reductive group and a parabolic. Following Drinfeld, one defines a (relative) compactification of the moduli stack of P-bundles on X. The present paper is concerned with the explicit description of the Intersection Cohomology sheaf of . The description is given in terms of the combinatorics of the Langlands dual Lie algebra
Mesoscopic Superconducting Disc with Short-Range Columnar Defects
Short-range columnar defects essentially influence the magnetic properties of
a mesoscopic superconducting disc.They help the penetration of vortices into
the sample, thereby decrease the sample magnetization and reduce the upper
critical field. Even the presence of weak defects split a giant vortex state
(usually appearing in a clean disc in the vicinity of the transition to a
normal state) into a number of vortices with smaller topological charges. In a
disc with a sufficient number of strong enough defects vortices are always
placed onto defects. The presence of defects lead to the appearance of
additional magnetization jumps related to the redistribution of vortices which
are already present on the defects and not to the penetration of new vortices.Comment: 14 pgs. RevTex, typos and figures corrected. Submitted to Phys. Rev.
Essential self-adjointness of magnetic Schr\"odinger operators on locally finite graphs
We give sufficient conditions for essential self-adjointness of magnetic
Schr\"odinger operators on locally finite graphs. Two of the main theorems of
the present paper generalize recent results of Torki-Hamza.Comment: 14 pages; The present version differs from the original version as
follows: the ordering of presentation has been modified in several places,
more details have been provided in several places, some notations have been
changed, two examples have been added, and several new references have been
inserted. The final version of this preprint will appear in Integral
Equations and Operator Theor
Surface Operators in Abelian Gauge Theory
We consider arbitrary embeddings of surface operators in a pure,
non-supersymmetric abelian gauge theory on spin (non-spin) four-manifolds. For
any surface operator with a priori simultaneously non-vanishing parameters, we
explicitly show that the parameters transform naturally under an SL(2, Z) (or a
congruence subgroup thereof) duality of the theory. However, for
non-trivially-embedded surface operators, exact S-duality holds only if the
quantum parameter effectively vanishes, while the overall SL(2, Z) (or a
congruence subgroup thereof) duality holds up to a c-number at most,
regardless. Via the formalism of duality walls, we furnish an alternative
derivation of the transformation of parameters - found also to be consistent
with a switch from Wilson to 't Hooft loop operators under S-duality. With any
background embedding of surface operators, the partition function and the
correlation functions of non-singular, gauge-invariant local operators on any
curved four-manifold, are found to transform like modular forms under the
respective duality groups.Comment: 30 pages. Minor refinemen
- …