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Showing 1 to 12 of 12 for “"Dihedral Group"”.
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The classification of the indecomposable integral representations of the dihedral group of order 2p
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 1962
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The Irreducible Representations of D2n
<p>Irreducible representations of a finite group over a field are important because all representations of a group are direct sums of irreducible representations. Maschke tells us that if φ is a representation of the finite group G of order n on the m-dimensional space V over the field K of complex …
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Soergel Diagrammatics for Dihedral Groups
… for the category of Soergel bimodules for the dihedral group W, finite or infinite. The (two-colored) Temperley-Lieb category is embedded inside this category as the degree 0 morphisms between color-alternating objects. The indecomposable Soergel bimodules are the images of Jones-Wenzl …
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On Proofs of Sylow's Theorem
… give a determination of conjugacy classes in the Dihedral group. We conclude with a sketch of Sylow.
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Fusion of Character Tables and Schur Rings of Dihedral Groups
A finite group H is said to fuse to a finite group G if the class algebra of G is isomorphic to an S-ring over H which is a subalgebra of the class algebra of H. We will also say that G fuses from H. In this case, the classes and characters of H can fuse to give the character table of G. We …
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Unitary representations of rational Cherednik algebras and Hecke algebras
… Cherednik algebras of complex reflection groups. We provide the complete classification of unitary representations for the symmetric group, the dihedral group, as well as some additional partial results. We also study the unitary representations of Hecke algebras of complex reflection …
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Average Cayley genus for Cayley maps with dihedral groups
Let Gamma be a finite group and let Delta be a generating set for Gamma. A Cayley map associated with Gamma and Delta is an oriented 2-cell embedding of the Cayley graph GDelta (Gamma) such that the rotation of arcs emanating from each vertex is determined by a unique cyclic permutation of …
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Groups, Graphs, and Symmetry-Breaking
… number of G. The distinguishing set of a group Gamma, D(Gamma), is the set of distinguishing numbers of graphs G in which Aut(G) = Gamma. It is shown that D(Gamma) is non-empty for any finite group Gamma. In particular, D(D<sub>n</sub>) is found where D<sub>n</sub> is the dihedral group …
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On Dihedral Codes and the Double Circulant Conjecture for Binary Extended Quadratic Residue Codes
… of length 2k as principal left ideals in the group algebra F2Dk where Dk is the dihedral group of order 2 k. We prove that these codes have a double circulant presentation in the following three cases: (1) q = 1. (2) q is a prime and 2 is a primitive root modulo q . (3) Let X be the class of x …
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The Classification of Automorphism Groups of Rational Elliptic Surfaces With Section
… give a classification of (regular) automorphism groups of relatively minimal rational elliptic surfaces with section over the field ℂ which have non-constant J-maps. The automorphism group Aut(B) of such a surface B is the semi-direct product of its Mordell-Weil group MW(B) and the subgroup …
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Minimum distance of error correcting codes versus encoding complexity, symmetry, and pseudorandomness
… sense of being invariant under the action of a group on the bits of the codewords. * The derandomization capabilities of probability measures on the Hamming cube based on binary linear codes with good distance properties, and their variations. Highlights of our results include: * A general …
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Exploring the multiplicative structure of Z/nZ
… n, is well known as a ring also as an additive group. In this thesis, we focus exclusively on its structure as a multiplicative monoid, when endowed with the multiplication only. To do this, our approach relies on the study of monoid homomorphisms. In particular, we investigate the homomorphisms …