Polynomial representation growth and the congruence subgroup problem
Polynomial representation growth and the congruence subgroup problem
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多项式表示增长和同余子群问题
DOI：
10.1007/bf02916715
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发表时间：
2004
影响因子：
1
通讯作者：
B. Martin
中科院分区：
文献类型：
--
作者：
A. Lubotzky;B. Martin
设Γ是半单群中的S-算术群。证明了若Γ具有同余子群性质，则Γ的n维不可约特征标的同构类个数是多项式有界的.在零特征中，匡威亦然。我们猜想，匡威也成立的积极的特点，我们证明了一些部分结果在这个方向上。
Let Γ be anS-arithmetic group in a semisimple group. We show that if Γ has the congruence subgroup property then the number of isomorphism classes of irreducible complexn-dimensional characters of Γ is polynomially bounded. In characteristic zero, the converse is also true. We conjecture that the converse also holds in positive characteristic, and we prove some partial results in this direction.