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Geometric Invariant Theory and Generalized Eigenvalue Problem II

Nicolas Ressayre (2011)

Annales de l’institut Fourier

Let $G$ be a connected reductive subgroup of a complex connected reductive group $\hat{G}$ . Fix maximal tori and Borel subgroups of $G$ and $\hat{G}$ . Consider the cone $ℒ ℛ^{\circ} (G, \hat{G})$ generated by the pairs $(ν, \hat{ν})$ of strictly dominant characters such that $V_{ν}^{*}$ is a submodule of $V_{\hat{ν}}$ . We obtain a bijective parametrization of the faces of $ℒ ℛ^{\circ} (G, \hat{G})$ as a consequence of general results on GIT-cones. We show how to read the inclusion of faces off this parametrization.

We develop the theory of associating moduli spaces with nice geometric properties to arbitrary Artin stacks generalizing Mumford’s geometric invariant theory and tame stacks.

Good properties of algebras of invariants and defect of linear representations.

Panyushev, Dmitri (1995)

Journal of Lie Theory

Displaying 1 – 6 of 6

Geometric Invariant Theory and Generalized Eigenvalue Problem II

Geometric invariant theory for general algebraic groups

GIT quotients of products of projective planes

Global Moduli for Surfaces of General Type.

Good moduli spaces for Artin stacks

Good properties of algebras of invariants and defect of linear representations.

Currently displaying 1 – 6 of 6