Geometric Invariant Theory and Generalized Eigenvalue Problem II
Copyright policy )Geometric Invariant Theory and Generalized Eigenvalue Problem II
Let G be a connected reductive subgroup of a complex connected reductive group G ^ . Fix maximal tori and Borel subgroups of G and G ^ . Consider the cone ℒ ℛ ∘ ( G , G ^ ) generated by the pairs ( ν , ν ^ ) of strictly dominant characters such that V ν * is a submodule of V ν ^ . We obtain a bijective parametrization of the faces of ℒ ℛ ∘ ( G , G ^ ) as a consequence of general results on GIT-cones. We show how to read the inclusion of faces off this parametrization.
Representation theory for linear algebraic groups, Moment polytope, Dolgachev-Hu G-ample cone, geometric invariant theory, 510, Mathematics - Algebraic Geometry, FOS: Mathematics, [MATH.MATH-RT] Mathematics [math]/Representation Theory [math.RT], Representation Theory (math.RT), Algebraic Geometry (math.AG), [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], Product of Belkale-Kumar, Horn problem, GIT-cone, Geometric Invariant Theory, generalized Horn problem, Littlewood-Richardson cone, Geometric invariant theory, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], branching rule, Mathematics - Representation Theory, Eigenvalue Problem
Representation theory for linear algebraic groups, Moment polytope, Dolgachev-Hu G-ample cone, geometric invariant theory, 510, Mathematics - Algebraic Geometry, FOS: Mathematics, [MATH.MATH-RT] Mathematics [math]/Representation Theory [math.RT], Representation Theory (math.RT), Algebraic Geometry (math.AG), [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], Product of Belkale-Kumar, Horn problem, GIT-cone, Geometric Invariant Theory, generalized Horn problem, Littlewood-Richardson cone, Geometric invariant theory, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], branching rule, Mathematics - Representation Theory, Eigenvalue Problem
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