HighestWeights : Table of Contents

• HighestWeights -- decompose free resolutions and graded modules with a semisimple Lie group action
• decomposeWeightsList -- decompose a list of weights into highest weights
• Example 1 -- The coordinate ring of the Grassmannian
• Example 2 -- The Buchsbaum-Rim complex
• Example 3 -- A multigraded Eagon-Northcott complex
• Example 4 -- The Eisenbud-Fløystad-Weyman complex
• Example 5 -- The singular locus of a symplectic invariant
• Example 6 -- The coordinate ring of the spinor variety
• Example 7 -- With the exceptional group G2
• Forward -- propagate weights from domain to codomain
• getWeights -- retrieve the (Lie theoretic) weight of a monomial
• getWeights(RingElement) -- retrieve the (Lie theoretic) weight of a monomial
• GroupActing -- stores the Dynkin type of the group acting on a ring
• highestWeightsDecomposition -- irreducible decomposition of a complex, ring, ideal or module
• highestWeightsDecomposition(...,Range=>...) -- decompose only part of a complex
• highestWeightsDecomposition(ChainComplex,ZZ,List) -- decompose an equivariant complex of graded free modules
• highestWeightsDecomposition(Ideal,List) -- decompose an ideal with a semisimple Lie group action
• highestWeightsDecomposition(Module,List,List) -- decompose a module with a semisimple Lie group action
• highestWeightsDecomposition(Ring,List) -- decompose a ring with a semisimple Lie group action
• LeadingTermTest -- check the columns of the input matrix for repeated leading terms
• LieWeights -- stores the (Lie theoretic) weights of the variables of a ring
• MinimalityTest -- check that the input map is minimal
• propagateWeights -- propagate (Lie theoretic) weights along equivariant maps
• propagateWeights(...,Forward=>...) -- propagate weights from domain to codomain
• propagateWeights(...,LeadingTermTest=>...) -- check the columns of the input matrix for repeated leading terms
• propagateWeights(...,MinimalityTest=>...) -- check that the input map is minimal
• propagateWeights(Matrix,List) -- propagate (Lie theoretic) weights along an equivariant map of graded free modules
• Range -- decompose only part of a complex
• setWeights -- attach (Lie theoretic) weights to the variables of a ring
• setWeights(PolynomialRing,DynkinType,List) -- attach (Lie theoretic) weights to the variables of a ring