1,267 research outputs found

    The spectra of finite 3-transposition groups

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    We calculate the spectrum of the diagram for each finite 33-transposition group. Such graphs with a given minimal eigenvalue have occurred in the context of compact Griess subalgebras of vertex operator algebras

    On primitive axial algebras of Jordan type

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    In this note we give an overview of our knowledge regarding primitive axial algebras of Jordan type half and connections between 33-transposition groups and Matsuo algebras. We also show that primitive axial algebras of Jordan type η\eta admit a Frobenius form, for any η\eta.Comment: 10 page

    General Eulerian Numbers and Eulerian Polynomials

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    In this paper, we will define general Eulerian numbers and Eulerian polynomials based on general arithmetic progressions. Under the new definitions, we have been successful in extending several well-known properties of traditional Eulerian numbers and polynomials to the general Eulerian polynomials and numbers.Comment: 14 page

    Experimental consequences of family unification

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    Theories of family unification predict four left-handed and four right-handed families of quarks and leptons, all with masses below 265 GeV. The lightest mirror quark has a mass of less than 140 GeV. All charged leptons are lighter than 55 GeV, and the lightest is below 40 GeV. All five new neutrinos have masses less than 40 GeV and contribute to the width of the Z0. We study the decays of these new families, and discuss rare processes such as μ→eγ. We also examine proton decay, and show that it can proceed into e+π0 at the observable but acceptable rate of 1032±1 yr
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