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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。 | |
We use the theory of tilting modules for algebraic groups to propose a characteristic free approach to "Howe duality" in the exterior algebra.
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The purpose of this note is to prove, as Lusztig stated, that the Euler characteristic of the variety of Iwahori subalgebras containing a certain nil-elliptic elementnt istcl wherel is the rank of the associated finite type Lie algebra.
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In our paper [KR] we began a systematic study of representations of the universal central extension[InlineEquation not available: see fulltext.] of the Lie algebra of differential operators on the circle.
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This study was continued in the paper [FKRW] in the framework of vertex algebra theory.
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The basic tool is the decomposition ofN pairs of free charged bosons with respect toglN and the commuting withglN Lie algebra of infinite matrices?l.
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The paper studies generic commutative and anticommutative algebras of a fixed dimension, their invariants, covariants and algebraic properties (e.g., the structure of subalgebras).
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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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In the case of 3-dimensional commutative algebras a new proof of a recent theorem of Katsylo and Mikhailov about the 28 bitangents to the associated plane quartic is given.
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We investigate such normal affine algebras in the case of a locally trivial action on a factorial variety.
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We give explicit systems of generators of the algebras of invariant polynomials in arbitrary many vector variables for the classical reflection groups (including the dihedral groups).
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We prove that the group of invertible elements of an irreducible algebraic monoid is an algebraic group, open in the monoid.
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We obtain a criterion for rational smoothness of an algebraic variety with a torus action, with applications to orbit closures in flag varieties, and to closures of double classes in regular group completions.
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For such maps, we prove the existence of an algebraic (?,+)-action φ on ?n for whichF is invariant.
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The action of an affine algebraic group G on an algebraic variety V can be
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Let k be a perfect field and G an algebraic group defined over k.
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We use the theory of tilting modules for algebraic groups to propose a characteristic free approach to "Howe duality" in the exterior algebra.
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The paper studies generic commutative and anticommutative algebras of a fixed dimension, their invariants, covariants and algebraic properties (e.g., the structure of subalgebras).
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Methods are developed for the calssification of homogeneous Riemannian hypersurfaces and the classification of linear transitive reductive algebraic group actions on pseudo-Riemannian hypersurfaces.
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This paper is devoted to a systematic study of quantum completely integrable systems (i.e., complete systems of commuting differential operators) from the point of view of algebraic geometry.
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We apply this criterion of algebraic integrability to two examples: finite-zone potentials and the elliptic Calogero-Moser system.
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