Arrangements of HyperplanesSpringer-Verlag, 1992 - 325页 |
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第235页
... invariants . ᄆ The polynomials which may be chosen as basic invariants for the irreducible unitary reflection groups were constructed by invariant theorists in the last century . The concept of a basic derivation is new . It is ...
... invariants . ᄆ The polynomials which may be chosen as basic invariants for the irreducible unitary reflection groups were constructed by invariant theorists in the last century . The concept of a basic derivation is new . It is ...
第240页
... invariants are algebraically independent , there exist unique polynomials i E C [ T1 , ...... , Te ] such that ( JTM ) ; , ; = Vi‚j ( ƒ1 , · · · , ƒe ) . Definition 6.67 Let F = { f1 , ... , fe } be a set of basic invariants and let ...
... invariants are algebraically independent , there exist unique polynomials i E C [ T1 , ...... , Te ] such that ( JTM ) ; , ; = Vi‚j ( ƒ1 , · · · , ƒe ) . Definition 6.67 Let F = { f1 , ... , fe } be a set of basic invariants and let ...
第281页
... invariants . For 1 ≤ i ≤l define 0 fi - 1 2 əfi მთ Dj . Then = { 0 , 0 } is the set of basic derivations associated to F. The notion of flat basic invariants was introduced in [ 202 ] . Recall from Definition 6.99 that de - 1 < de ...
... invariants . For 1 ≤ i ≤l define 0 fi - 1 2 əfi მთ Dj . Then = { 0 , 0 } is the set of basic derivations associated to F. The notion of flat basic invariants was introduced in [ 202 ] . Recall from Definition 6.99 that de - 1 < de ...
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A₁ affine arrangement algebra A(A arrangement and let assume b₁ basic derivations basic invariants basis for D(A braid arrangement broken circuit central arrangement chain complex choose cohomology complement complex reflection groups complexification compute Corollary Coxeter group defining polynomial Definition deformation retraction degree denote dependent exact sequence Example exterior algebra exterior product fiber finite follows from Lemma follows from Proposition follows from Theorem formula free arrangement free with exp G-orbit graded K-module graph H₁ H₂ homogeneous homotopy type hyperplanes inductively free integers irreducible isomorphism K-algebra ker(x l-arrangement lattice Lemma Let G linear linearly independent matrix maximal element Möbius function modular elements module N¹(A nonempty Note Orbits Poincaré polynomial poset Proof prove real arrangement Recall reflection arrangement restriction result Saito's criterion 4.19 Section Shephard groups simplicial subset subspace supersolvable supersolvable arrangement Suppose surjective vertex w₁ write x-independent