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Weyl Closure of a Linear Differential Operator

✍ Scribed by Harrison Tsai

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
382 KB
Volume
29
Category
Article
ISSN
0747-7171

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✦ Synopsis

We study the Weyl closure Cl(L) = K(x) βˆ‚ L ∩ D for an operator L of the first Weyl algebra D = K x, βˆ‚ . We give an algorithm to compute Cl(L) and we describe its initial ideal under the order filtration. Our main application is an algorithm for constructing a Jordan-HΓΆlder series for a holonomic D-module and a formula for its length. Using the closure, we also reproduce a result of , who described the initial ideals of left ideals of D under the order filtration, and a result of , who described the isomorphism classes of right ideals of D.

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