Search results for "Mathematics::Representation Theory"

showing 3 items of 113 documents

IRREDUCIBLE COXETER GROUPS

2004

We prove that a non-spherical irreducible Coxeter group is (directly) indecomposable and that an indefinite irreducible Coxeter group is strongly indecomposable in the sense that all its finite index subgroups are (directly) indecomposable. Let W be a Coxeter group. Write W = WX1 × ⋯ × WXb × WZ3, where WX1, … , WXb are non-spherical irreducible Coxeter groups and WZ3 is a finite one. By a classical result, known as the Krull–Remak–Schmidt theorem, the group WZ3 has a decomposition WZ3 = H1 × ⋯ × Hq as a direct product of indecomposable groups, which is unique up to a central automorphism and a permutation of the factors. Now, W = WX1 × ⋯ × WXb × H1 × ⋯ × Hq is a decomposition of W as a dir…

[ MATH.MATH-GR ] Mathematics [math]/Group Theory [math.GR]General MathematicsGroup Theory (math.GR)0102 computer and information sciencesPoint group01 natural sciences[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]CombinatoricsMathematics::Group TheoryFOS: Mathematics0101 mathematicsLongest element of a Coxeter groupMathematics::Representation Theory[MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]MathematicsMathematics::CombinatoricsCoxeter notationMathematics::Rings and Algebras010102 general mathematicsCoxeter group010201 computation theory & mathematicsCoxeter complexArtin group20F55Indecomposable moduleMathematics - Group TheoryCoxeter elementInternational Journal of Algebra and Computation
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A note on the Lawrence-Krammer-Bigelow representation

2002

A very popular problem on braid groups has recently been solved by Bigelow and Krammer, namely, they have found a faithful linear representation for the braid group B_n. In their papers, Bigelow and Krammer suggested that their representation is the monodromy representation of a certain fibration. Our goal in this paper is to understand this monodromy representation using standard tools from the theory of hyperplane arrangements. In particular, we prove that the representation of Bigelow and Krammer is a sub-representation of the monodromy representation which we consider, but that it cannot be the whole representation.

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Pure mathematicsLinear representation[ MATH.MATH-GR ] Mathematics [math]/Group Theory [math.GR]Braid group20F36Group Theory (math.GR)52C3001 natural sciences[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]52C35Mathematics - Geometric TopologyMathematics::Group TheoryMathematics::Algebraic Geometry[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesFOS: Mathematics20F36 52C35 52C30 32S22braid groups0101 mathematicsMathematics::Representation TheoryComputingMilieux_MISCELLANEOUSMathematics[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT][MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]linear representations010102 general mathematicsRepresentation (systemics)FibrationSalvetti complexesGeometric Topology (math.GT)Mathematics::Geometric TopologyHyperplaneMonodromy010307 mathematical physicsGeometry and TopologyMathematics - Group Theory32S22
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Jeu de Taquin and Diamond Cone for so(2n+1, C)

2020

International audience; The diamond cone is a combinatorial description for a basis of a natural indecomposable n-module, where n is the nilpotent factor of a complex semisimple Lie algebra g. After N. J. Wildberger who introduced this notion, this description was achieved for g = sl(n) , the rank 2 semisimple Lie algebras and g = sp (2n).In this work, we generalize these constructions to the Lie algebra g = so(2n + 1). The orthogonal semistandard Young tableaux were defined by M. Kashiwara and T. Nakashima, they index a basis for the shape algebra of so(2n + 1). Defining the notion of orthogonal quasistandard Young tableaux, we prove that these tableaux describe a basis for a quotient of t…

quasistandard Young tableauMathematics::Quantum AlgebraShape algebrajeu de taquinMSC: 20G05 05A15 17B10[MATH] Mathematics [math][MATH]Mathematics [math]Mathematics::Representation Theorysemistandard Young tableau
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