The decomposition numbers of the hecke algebra of type F4

Meinolf Geck, Klaus Lux

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

Let W be the finite Coxeter group of type F4, and Hrq 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 HRq 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 F4 over the ring A = ℤ[u1/2, u-1/2] of Laurent polynomials in an indeterminate u1/2 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

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'The decomposition numbers of the hecke algebra of type F<sub>4</sub>'. Together they form a unique fingerprint.

Cite this