Plotkin E., Semenov A. & Vavilov N., Visual basic representations: an atlas, Internat. J. Algebra Comput. 8 (1998), 61--95. Home/Search Document Details and Download
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A Third Look At Weight Diagrams - Vavilov (3 citations) Self-citation (Vavilov) (Correct)
....THIRD LOOK AT WEIGHT DIAGRAMS Nikolai Vavilov Department of Mathematics and Mechanics University of Sanct Petersburg Petrodvorets, 198904, Russia Abstract. In this paper, which is a sequel of [PSV], we develop a completely elementary approach to calculations in Chevalley groups G = G( Phi; R) of types Phi = E 6 and E 7 over a commutative ring R using only the weight diagrams (alias, crystal graphs) of their minimal modules. After an elementary construction of a crystal base we explicitly ....
.... representations, apart from a unique representation for each type, are microweight [B2] i.e. they do not have zero weight, so that the weights in fact form a single Weyl orbit, as in the above cases (E 6 ; 1 ) and (E 7 ; 7 ) Diagrams of all basic and adjoint representations are collected in [PSV]. These diagrams arise in a number of contexts, ranging from representation theory of semisimple Lie algebras and algebraic groups to invariant theory, algebraic geometry, algebraic K theory, differential geometry and combinatorics. One can find detailed discussion of the diagrams and some of ....
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Plotkin E.B., Semenov A.A., Vavilov N.A., Visual basic representations: an atlas, Int. J. Algebra and Computations 8 (1998), no. 1, 61--97.
Paths in Weyl chambers and random matrices - Bougerol, Jeulin (4 citations) (Correct)
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Plotkin E., Semenov A. & Vavilov N., Visual basic representations: an atlas, Internat. J. Algebra Comput. 8 (1998), 61--95.
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