Titlebook: Collected Papers; Volume I 1955-1966 Bertram Kostant,Anthony Joseph,Shrawan Kumar,Michè Book 2009 The Editor(s) (if applicable) and The Aut

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On Differential Geometry and Homogeneous Spaces II,We retain the notation of the preceding paper.. We will say that . is effective relative to . if . contains no ideal of ..

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A Characterization of the Classical Groups,By one method of classification there are three types of (complex, connected) classical groups, (a) .(.), (b) .(.), and (c) .(.). So designated, each type is given as a specific group of matrices. It is perhaps neater (and for us more pertinent) to describe these groups by means of the special linear representation which each type admits.

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The Principal Three-Dimensional Subgroup and the Betti Numbers of a Complex Simple Lie Group,Let . be a complex simple Lie algebra and let . be the adjoint group of g. It is by now classical that the Poincaré polynomial ..(.) of . factors into the form

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Lie Group Representations On Polynomial Rings,Let . be a group of linear transformations on a finite dimensional real or complex vector space .. Assume . is completely reducible as a .-module. Let . be the ring of all complex-valued polynomials on ., regarded as a .-module in the obvious way, and let . ? . be the subring of all .-invariant polynomials on ..

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Lie Group Representations on Polynomial Rings,Let . be a group of linear transformations on a finite dimensional real or complex vector space .. Assume . is completely reducible as a .-module. Let . be the ring of all complex-valued polynomials on ., regarded as a .-module in the obvious way, and let . ? . be the sub-ring of all .-invariant polynomials on ..

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Lie Algebra Cohomology and Generalized Schubert Cells,This paper is referred to as Part II. Part I is [4], The numerical I used as a reference will refer to that paper. A third and final part, . is also planned.

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