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| 复反射群G(m,p,r)的陪集分解 |
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徐静蕾1,2, 王彦杰1,3, 王丽1
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1.上海师范大学数理学院, 上海, 200234;2.上海大学附属中学, 上海, 200444;3.常熟中学, 江苏, 常熟, 215516
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| 摘要: |
| 本文研究了非本原复反射群G（m，p，r）的右陪集分解，其中m，p，r是正整数，且p整除m.通过使用GAP软件计算一些当m，p，r取较小自然数时的特例，推导出了一般情形下，非本原复反射群G（m，p，r）的抛物型子群G（m，p，r-1）的一个完全的右陪集代表元集，这个结果为进一步研究G（m，p，r-1）在G（m，p，r）中的特异右陪集代表元集打下基础. |
| 关键词: 右陪集代表 非本原复反射群 |
| DOI： |
| 分类号:O152.3 |
| 基金项目: |
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| ON COSET DECOMPOSITIONS OF THE COMPLEX REFLECTION GROUPS G(M, P, R) |
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XU Jing-lei1,2, WANG Yan-jie1,3, WANG Li1
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1.School of Mathematics and Science, Shanghai Normal University, Shanghai 200234, China;2.The A-liated High School of Shanghai University, Shanghai 200444, China;3.Changshu High School, Changshu 215516, China
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| Abstract: |
| We study the decomposition of the imprimitive complex reflection group G(m, p, r) into right coset, where m, p, r are positive integers, and p divides m. By use of the software GAP to compute some special cases when m, p, r are small integers, we deduce a set of complete right coset representatives of the parabolic subgroup G(m, p, r-1) in the group G(m, p, r) for general cases, which lays a foundation for further study the distinguished right coset representatives of G(m, p, r-1) in G(m, p, r). |
| Key words: right coset representatives imprimitive complex reflection groups |
