For given operators A ∈ B(H), B ∈ B(K), we investigate the intersection of Weyl spectra ∩_(C∈B_(K,H)) σ_w(M_C) by analyse the spectrum structure of operators and give a complete characterization of the intersection of Browder spectra ∩_(C∈B_(K,H)) σ_b(M_C).
An algebraicG-varietyX is called "wonderful", if the following conditions are satisfied:X is (connected) smooth and complete;X containsr irreducible smoothG-invariant divisors having a non void transversal intersection;G has 2r orbits inX.
We apply these results to intersection theory on varieties with group actions, especially to Schubert calculus and its generalizations.
We give criteria for a divisor to be Cartier, globally generated and ample, and apply them to a study of the local structure and the intersection theory of aG-variety.
However the compatibility of the canonical base of the modified algebra and of the geometric base given by intersection cohomology sheaves on the affine flag variety was never proved.
We derive two consequences: the first is a new proof of Lusztig's description of the intersection cohomology of nilpotent orbit closures for GLn, and the second is an analogous description for GL2n/Sp2n.