The questions that have been at the center of invariant theory since the 19th century have
revolved around the following themes: finiteness, computation, and special classes of …

Let $ K $ be a compact Lie group with complexification $ G $, and let $ V $ be a unitary $ K $-
module. We consider the real symplectic quotient $ M_ {0} $ at level zero of the …

Let p: G—> GL (V) be a rational representation of a reductive algebraic group over the
algebraically closed field k. The action of G on V induces an action of G on k [V], the algebra …

Abstract Let K→U(V) be a unitary representation of the compact Lie group K. Then there is a
canonical moment mapping ρ:V→\mathfrakk^*. We have the Koszul complex K(ρ,C^∞(V)) of …

On a smoothness characterization for good moduli spaces - ScienceDirect Skip to main
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For a subgroup $ H $ of a reductive group $ G $, let $\mathfrak m\subset\mathfrak g^* $ be
the cotangent space of $ eH\in G/H $. The linear action $(H:\mathfrak m) $ is the coisotropy …

We develop a theory of toric Artin stacks extending the theories of toric Deligne–Mumford
stacks developed by Borisov–Chen–Smith, Fantechi–Mann–Nironi, and Iwanari. We also …

We compute the Hilbert series of the graded algebra of real regular functions on a linear
symplectic quotient by the 2-torus as well as the first four coefficients of the Laurent …

Abstract Let ρ: T→ GL (V) be a finite dimensional rational representation of a torus over an
algebraically closed field k. We give necessary and sufficient conditions on the arrangement …

Let V be a finite-dimensional representation of the complex circle C× determined by a weight
vector a∈ Z n. We study the Hilbert series Hilb a (t) of the graded algebra C [V] C a× of …