ar X iv : 0 81 1 . 22 73 v 1 [ m at h . FA ] 1 4 N ov 2 00 8 Products of Longitudinal Pseudodifferential Operators on Flag Varieties
نویسنده
چکیده
Associated to each set S of simple roots for SL(n, C) is an equivariant fibration X → XS of the space X of complete flags of C n. To each such fi-bration we associate an algebra JS of operators on L 2 (X) which contains, in particular, the longitudinal pseudodifferential operators of negative order tangent to the fibres. These form a lattice of operator ideals whose common intersection is the compact operators. As a consequence, the product of fibrewise smoothing operators (for instance) along the fibres of two such fibrations, X → XS and X → XT , is a compact operator if S ∪ T is the full set of simple roots. The construction 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'.
منابع مشابه
ar X iv : 0 81 1 . 22 73 v 2 [ m at h . FA ] 1 5 N ov 2 00 8 Products of Longitudinal Pseudodifferential Operators on Flag Varieties
Associated to each set S of simple roots for SL(n, C) is an equivariant fibration X → XS of the space X of complete flags of C n. To each such fi-bration we associate an algebra JS of operators on L 2 (X) which contains, in particular, the longitudinal pseudodifferential operators of negative order tangent to the fibres. These form a lattice of operator ideals whose common intersection is the c...
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