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

Meinolf Geck () and Jürgen Müller ()
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Meinolf Geck: Universität Stuttgart, IAZ-Lehrstuhl für Algebra
Jürgen Müller: Bergische Universität Wuppertal, Arbeitsgruppe Algebra und Zahlentheorie

A chapter in Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, 2017, pp 311-360 from Springer

Abstract: 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.

Keywords: Iwahori-Hecke algebras; Balanced representations; W-graph representations; Invariant forms; Integral linear algebra; Linear algebra over polynomial rings; MeatAxe philosophy; 20C08; 20C40 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-70566-8_13

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DOI: 10.1007/978-3-319-70566-8_13

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