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Showing 1 to 11 of 11 for “"D-modules,"”.
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Lie Algebras of Differential Operators and D-modules
In our thesis we study the algebras of differential operators in algebraic and geometric terms. We consider two problems in which the algebras of differential operators naturally arise. The first one deals with the algebraic structure of differential and pseudodifferential operators. We define the …
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D-modules, V-filtrations, and B-functions in mixed characteristic
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2023-12-04 without embargo terms
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Categorification of the Kirwan map
… it is shown that the equivariant category of D-modules with certain support condition is equivalent to the category of D-modules on the quotient. It is then shown that we can associate particular equivariant D-modules to characters of the group and these equivariant D-modules are compatible in a …
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Connections on conformal blocks
… a projective curve X, we study the category of D-modules on the moduli space Bung of principal G-bundles on X using ideas from conformal field theory. We describe this category in terms of the action of infinitesimal Hecke functors on the category of quasi-coherent sheaves on Bung. This family of …
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D-cap modules on rigid analytic spaces
… for coadmissible $\wideparen{\mathcal{D}}$-modules on rigid analytic spaces. Our main result is a $\wideparen{\mathcal{D}}$-module analogue of Kiehl's Proper Mapping Theorem, considering the 'naive' pushforward from $\wideparen{\mathcal{D}}_X$-modules to …
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Equivariant line bundles with connection on the Drinfeld upper half-space Ω⁽²⁾
… and Wadsley developed a theory of $\mathscr{D}$-modules on rigid analytic spaces and established a Beilinson-Bernstein style localisation theorem for coadmissible modules over the locally analytic distribution algebra. Using this theory, they obtained admissible locally analytic representations …
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On trigonometric and elliptic Cherednik algebras
… a functor from the category of Harish- Chandra modules of the symmetric pair of type AIII to the category of representations of the degenerate affine and double affine Hecke algebra of type BC. We also study the images of some D-modules and the principal series modules. In the second part, we …
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Promoting the Emergence of Advance Knowledge (Peak) Relational Training System: Exploring the Practical Implementation of the Generalization Training and Direct Training Modules
… System’s Generalization and Direct Training modules in a practical setting across two studies. Study 1 investigated whether a relationship exists between the PEAK-G and PEAK-D Training protocols, if the skills mastered through these would generalize to the natural environment, and whether …
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Rigid Analytic Quantum Groups
… We define a category of $\lambda$-twisted $D$-modules on this analytic quantum flag variety. This category has a distinguished object $\widehat{\D_q^\lambda}$ which plays the role of the sheaf of $\lambda$-twisted differential operators. We show that when $\lambda$ is regular and dominant, the …
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Representation theory of the global Cherednik algebra
… functor from the category of P-coherent modules for the Cherednik algebra to finite dimensional modules over the Hecke algebra is essentially surjective. Then we begin to use this result to study the analog of category 0 for Cherednik algebras on Riemann surfaces and on products of …
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On a Heegaard Floer theory for tangles
… structure in terms of (what we call) peculiar modules. Together with a glueing theorem, we can easily recover oriented and unoriented skein relations for HFL^. Our peculiar modules also enjoy some symmetry relations, which support a conjecture about δ-graded mutation invariance of HFL^. …