The decomposition numbers of the hecke algebra of typeF4
The decomposition numbers of the hecke algebra of typeF4
复制标题
F4型赫克代数的分解数
DOI：
10.1007/bf02568379
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发表时间：
1991
影响因子：
0.6
通讯作者：
Klaus Lux
中科院分区：
文献类型：
--
作者：
M. Geck;Klaus Lux
设W是F4型有限Coxeter群，Hr（q）是定义在Q的一个足够大的扩张域中的赋值环R上的相伴Hecke代数，参数为一个素幂q，剩余类域为特征r.本文确定了HR（q）对q和r的模分解数，使得r不整除q。证明方法包括研究不定u ~（1/2）中Laurent多项式环A =[u ~（1/2），u ~（1/2）]上的F_4型通有Hecke代数及其在各种分圆数域上的整数环上的特殊化。计算机和计算机程序系统（GAP、MAPLE、Meat-Axe）得到了大量使用。
LetW be the finite Coxeter group of typeF4, andHr(q) be the associated Hecke algebra, with parameter a prime powerq, defined over a valuation ringR in a large enough extension field ofQ, with residue class field of characteristicr. In this paper, ther-modular decomposition numbers ofHR(q) are determined for allq andr such thatr does not divideq. The methods of the proofs involve the study of the generic Hecke algebra of typeF4 over the ringA = ℤ[u1/2,u-1/2] of Laurent polynomials in an indeterminateu1/2 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.