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- W2962912261 abstract "Associated to each set S of simple roots of SL ( n , C ) is an equivariant fibration X → X S of the complete flag variety X of C n . To each such fibration we associate an algebra J S of operators on L 2 ( X ) , or more generally on L 2 -sections of vector bundles over X . This ideal contains, in particular, the longitudinal pseudodifferential operators of negative order tangent to the fibres. Together, they form a lattice of operator ideals whose common intersection is the compact operators. Thus, for instance, the product of negative order pseudodifferential operators along the fibres of two such fibrations, X → X S and X → X T , is a compact operator if S ∪ T is the full set of simple roots. The construction of the ideals uses noncommutative harmonic analysis, and hinges upon a representation theoretic property of subgroups of SU ( n ) , which may be described as ‘essential orthogonality of subrepresentations’." @default.
- W2962912261 created "2019-07-30" @default.
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- W2962912261 date "2010-02-01" @default.
- W2962912261 modified "2023-10-17" @default.
- W2962912261 title "Products of longitudinal pseudodifferential operators on flag varieties" @default.
- W2962912261 cites W2062632751 @default.
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- W2962912261 doi "https://doi.org/10.1016/j.jfa.2009.10.007" @default.
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