NDLI: Characters of equivariant -modules on spaces of matrices

Content Provider	Scilit
Author	Raicu, Claudiu
Copyright Year	2016
Description	Journal: Compositio Mathematica We compute the characters of the simple $\text{GL}$-equivariant holonomic ${\mathcal{D}}$-modules on the vector spaces of general, symmetric, and skew-symmetric matrices. We realize some of these ${\mathcal{D}}$-modules explicitly as subquotients in the pole order filtration associated to the $\text{determinant}/\text{Pfaffian}$ of a generic matrix, and others as local cohomology modules. We give a direct proof of a conjecture of Levasseur in the case of general and skew-symmetric matrices, and provide counterexamples in the case of symmetric matrices. The character calculations are used in subsequent work with Weyman to describe the ${\mathcal{D}}$-module composition factors of local cohomology modules with determinantal and Pfaffian support.
Ending Page	1965
Starting Page	1935
ISSN	00221295
e-ISSN	15705846
DOI	10.1112/s0010437x16007521
Journal	Compositio Mathematica
Issue Number	9
Volume Number	152
Language	English
Publisher	Wiley-Blackwell
Publisher Date	2016-09-01
Access Restriction	Open
Subject Keyword	Journal: Compositio Mathematica Mathematical Physics
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory

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Characters of equivariant -modules on spaces of matrices