<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="script">D</mml:mi></mml:math>-modules on representations of Capelli type

Nang, Philibert

doi:10.1016/j.jalgebra.2016.12.029

Journal of Algebra

2017

DOI: 10.1016/j.jalgebra.2016.12.029

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D-modules on representations of Capelli type

Philibert Nang

Abstract: We give an answer to the abstract Capelli problem: Let (G, V ) be a multiplicity-free finitedimensional representation of a connected reductive complex Lie Group G and G ′ be its derived subgroup. Assume that the categorical quotient V //G is one-dimensional , i.e., there exists a polynomial f generating the algebra of

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2019

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On categories of equivariant D-modules

Lörincz¹,

Walther²

2019

Advances in Mathematics

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Let X be a variety with an action by an algebraic group G. In this paper we discuss various properties of G-equivariant D-modules on X, such as the decompositions of their global sections as representations of G (when G is reductive), and descriptions of the categories that they form. When G acts on X with finitely many orbits, the category of equivariant D-modules is equivalent to the category of finite-dimensional representations of a finite quiver with relations. We describe explicitly these categories for irreducible G-modules X that are spherical varieties, and show that in such cases the quivers are almost always representation-finite (i.e. with finitely many indecomposable representations).

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On categories of equivariant D-modules

Lörincz¹,

Walther²

2019

Advances in Mathematics

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D-modules on representations of Capelli type

Cited by 1 publication

References 34 publications

On categories of equivariant D-modules

On categories of equivariant D-modules

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