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Algorithms in Linear Algebraic Groups

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Abstract

This paper presents some algorithms in linear algebraic groups. These algorithms solve the word problem and compute the spinor norm for orthogonal groups. This gives us an algorithmic definition of the spinor norm. We compute the double coset decomposition with respect to a Siegel maximal parabolic subgroup, which is important in computing infinite-dimensional representations for some algebraic groups.

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Acknowledgements

We are indebted to the anonymous referees for their careful reading. Their comments and suggestions improved this paper. This work was supported by a SERB research Grant.

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Authors and Affiliations

  1. IISER Mohali, Knowledge city, Sector 81, SAS Nagar, Manauli, Punjab, 140306, India

    Sushil Bhunia

  2. IISER Pune, Dr. Homi Bhabha Road, Pashan, Pune, 411008, India

    Ayan Mahalanobis, Pralhad Shinde & Anupam Singh

Authors
  1. Sushil Bhunia
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  2. Ayan Mahalanobis
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  3. Pralhad Shinde
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  4. Anupam Singh
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Correspondence to Ayan Mahalanobis.

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This article is part of the Topical Collection on 2019 Alterman Conference on Geometric Algebra/Kahler Calculus, edited by Harikrishnan Panackal.

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Bhunia, S., Mahalanobis, A., Shinde, P. et al. Algorithms in Linear Algebraic Groups. Adv. Appl. Clifford Algebras 30, 31 (2020). https://doi.org/10.1007/s00006-020-01054-y

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