1,084 research outputs found
Microlocal Euler classes and Hochschild homology
We define the notion of a trace kernel on a manifold M. Roughly speaking, it
is a sheaf on M x M for which the formalism of Hochschild homology applies. We
associate a microlocal Euler class to such a kernel, a cohomology class with
values in the relative dualizing complex of the cotangent bundle over M and we
prove that this class is functorial with respect to the composition of kernels.
This generalizes, unifies and simplifies various results of (relative) index
theorems for constructible sheaves, D-modules and elliptic pairs.Comment: The proof of Theorem 4.6 has been considerably simplified. To appear
in the Journal of the Institute of Mathematics of Jussie
Quantization of complex Lagrangian submanifolds
Let be a smooth Lagrangian submanifold of a complex symplectic
manifold . We construct twisted simple holonomic modules along in
the stack of deformation-quantization modules on
On the de Rham complex of mixed twistor D-modules
Given a complex manifold S, we introduce for each complex manifold X a
t-structure on the bounded derived category of C-constructible complexes of
O_S-modules on X x S. We prove that the de Rham complex of a holonomic
D_{XxS/S}-module which is O_S-flat as well as its dual object is perverse
relatively to this t-structure. This result applies to mixed twistor D-modules.Comment: 18 page
Perfect Crystals for U_q(D_4^{(3)})
A perfect crystal of any level is constructed for the Kirillov-Reshetikhin
module of corresponding to the middle vertex of the Dynkin
diagram. The actions of Kashiwara operators are given explicitly. It is also
shown that this family of perfect crystals is coherent. A uniqueness problem
solved in this paper can be applied to other quantum affine algebras.Comment: 27 page
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