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Explicit Equations for Exterior Square of the General Linear Group

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Several explicit systems of equations defining the exterior square of the general linear group ⋀2 GLn as affine group scheme are presented. Algebraic ingredients of the equations, so called exterior numbers, are translated to the language of weight diagrams corresponding to a Lie group of type An−1 in the representation with the highest weight ϖ2.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    R. A. Lubkov

  2. The Chebyshev Laboratory, St.Petersburg State University, St.Petersburg, Russia

    I. I. Nekrasov

Authors
  1. R. A. Lubkov
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  2. I. I. Nekrasov
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Correspondence to R. A. Lubkov.

Additional information

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 470, 2018, pp. 120–137.

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Lubkov, R.A., Nekrasov, I.I. Explicit Equations for Exterior Square of the General Linear Group. J Math Sci 243, 583–594 (2019). https://doi.org/10.1007/s10958-019-04559-5

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  • DOI: https://doi.org/10.1007/s10958-019-04559-5

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