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|  | | 为了更好的帮助您理解掌握查询词或其译词在地道英语中的实际用法,我们为您准备了出自英文原文的大量英语例句,供您参考。 | |
In the second example, we obtain a proof of the Chalyh-Veselov conjecture that the Calogero-Moser system with integer parameter is algebraically integrable, using the results of Felder and Varchenko.
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As an application of the results we prove a generalization of Chevalley's restriction theorem for the classical Lie algebras.
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We apply these results to intersection theory on varieties with group actions, especially to Schubert calculus and its generalizations.
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In this paper, we prove three types of rigidity results related to CAT(-1) spaces, namely the rigidity of the isometric actions on CAT(-1) spaces under the commensurability subgroups, the higher rank lattices and certain ergodic cocycles.
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This extends the results and simplifies the proof for the classical orbit structure description of [10] and [11], which applies whenF=Z.
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They result in many nontrivial properties of quantum immanants.
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We prove the following result: LetG be a finite irreducible linear group.
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The proof is an application of a recent result by W.
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We prove as the main result thatM is weakly symmetric with respect toG1 and complex conjugation.
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As a result, this provides new examples of weakly symmetric spaces that are nonsymmetric, including those already discovered by Selberg (cf.
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A basis is calledmonomial if each of its elements is the result of applying to a (fixed) highest weight vector a monomial in the Chevalley basis elementsYα, α a simple root, in the opposite Borel subalgebra.
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The result generalizes and implies the classical "branching rules" that describe the restriction of an irreducible representation of the symmetric groupSn toSn-1.
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Implementing this point of view, Poisson Summation Formulas are proved in several spaces including integrable functions of bounded variation (where the result is known) and elements of mixed norm spaces.
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We use interpolation methods to prove a new version of the limiting case of the Sobolev embedding theorem, which includes the result of Hansson and Brezis-Wainger for Wnk/k as a special case.
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The weighted inequalities allow us to transfer the result to the ergodic case, when the operator is induced by a mean bounded, invertible, positive groups.
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In the case of 4-dimensional anticommutative algebras a construction is given that links the associated cubic surface and the 27 lines on it with the structure of subalgebras of the algebra.
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Such an action is called linearizable if it is equivalent to the restriction of a linear orthogonal action in the ambient affine space of the quadric.
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In general the group ring of ann-valued group is not ann-Hopf algebra but it is for ann-coset group constructed from an abelian group.
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From it, we recover Joseph and Letzter's result by a kind of "quantum duality principle".
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It is well-known that the ring of invariants associated to a non-modular representation of a finite group is Cohen-Macaulay and hence has depth equal to the dimension of the representation.
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