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Invariant Bilinear Forms on W-Graph Representations and Linear Algebra Over Integral Domains

In: Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory

Author

Listed:
  • Meinolf Geck

    (Universität Stuttgart, IAZ-Lehrstuhl für Algebra)

  • Jürgen Müller

    (Bergische Universität Wuppertal, Arbeitsgruppe Algebra und Zahlentheorie)

Abstract

Lie-theoretic structures of type E 8 (e.g., Lie groups and algebras, Iwahori–Hecke algebras and Kazhdan–Lusztig cells, …) are considered to serve as a “gold standard” when it comes to judging the effectiveness of a general algorithm for solving a computational problem in this area. Here, we address a problem that occurred in our previous work on decomposition numbers of Iwahori–Hecke algebras, namely, the computation of invariant bilinear forms on so-called W-graph representations. We present a new algorithmic solution which makes it possible to produce and effectively use the main results in further applications.

Suggested Citation

  • Meinolf Geck & Jürgen Müller, 2017. "Invariant Bilinear Forms on W-Graph Representations and Linear Algebra Over Integral Domains," Springer Books, in: Gebhard Böckle & Wolfram Decker & Gunter Malle (ed.), Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, pages 311-360, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-70566-8_13
    DOI: 10.1007/978-3-319-70566-8_13
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