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

DOI10.1007/978-3-319-70566-8_13zbMath1423.20004arXiv1701.02331OpenAlexW2612736133MaRDI QIDQ4556579

Meinolf Geck, Jürgen Müller

Publication date: 16 November 2018

Published in: Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.02331

zbMATH Keywords

Iwahori-Hecke algebrasinvariant formsbalanced representations\(W\)-graph representationsintegral linear algebralinear algebra over polynomial ringsMeatAxe philosophy

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) Bilinear and Hermitian forms (11E39)

Uses Software

• GAP
• gmp
• CHEVIE

Cites Work

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• Representations of Hecke algebras at roots of unity.
• James' conjecture for Hecke algebras of exceptional type. I.
• Computational construction of irreducible \(W\)-graphs for types \(E_6\) and \(E_7\).
• Exact solution of linear equations using p-adic expansions
• Representations of Coxeter groups and Hecke algebras
• CHEVIE -- A system for computing and processing generic character tables
• The development version of the \texttt{CHEVIE} package of \texttt{GAP3}.
• $E_8$, the most exceptional group
• Modern Computer Algebra
• Leading coefficients and cellular bases of Hecke algebras
• P-adic reconstruction of rational numbers
• Maximal quotient rational reconstruction
• Hecke Algebras with Unequal Parameters
• On the Kazhdan–Lusztig cells in type $E_8$

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