The decomposition numbers of the hecke algebra of type F 4

Meinolf Geck, Klaus M Lux

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

Let W be the finite Coxeter group of type F 4, and H r (q) be the associated Hecke algebra, with parameter a prime power q, defined over a valuation ring R in a large enough extension field of Q, with residue class field of characteristic r. In this paper, the r-modular decomposition numbers of H R (q) are determined for all q and r such that r does not divide q. The methods of the proofs involve the study of the generic Hecke algebra of type F 4 over the ring A = ℤ[u 1/2, u -1/2] of Laurent polynomials in an indeterminate u 1/2 and its specializations onto the ring of integers in various cyclotomic number fields. Substancial use of computers and computer program systems (GAP, MAPLE, Meat-Axe) has been made.

Original languageEnglish (US)
Pages (from-to)285-306
Number of pages22
JournalManuscripta Mathematica
Volume70
Issue number1
DOIs
StatePublished - Dec 1991
Externally publishedYes

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Hecke Algebra
Cyclotomic numbers
Modular Decomposition
Ring
Decompose
Cyclotomic Fields
Laurent Polynomials
Valuation Ring
Field extension
Coxeter Group
Specialization
Number field
Divides
Finite Group
Integer
Class

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The decomposition numbers of the hecke algebra of type F 4. / Geck, Meinolf; Lux, Klaus M.

In: Manuscripta Mathematica, Vol. 70, No. 1, 12.1991, p. 285-306.

Research output: Contribution to journalArticle

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