Theta series of unimodular lattices, combinatorial identities and weighted symmetric polynomials
文献类型：期刊论文
| 作者 | Xu, XP
|
| 刊名 | ALGEBRA COLLOQUIUM
 |
| 出版日期 | 2006-03-01 |
| 卷号 | 13期号:1页码:67-86 |
| 关键词 | unimodular lattices theta series combinatorial identities symmetric polynomials root lattices |
| ISSN号 | 1005-3867 |
| 英文摘要 | Hecke proved that the theta series of a positive definite even unimodular lattice is a polynomial of the well-known Essenstein series E-4(z) and the Ramanujan series Delta(24)(z). A natural question is what kind of polynomials in E-4(z) and Delta(24)(Z) could be the theta series of positive definite even unimodular lattices. In this paper, we find two combinatorial identities on the theta series of the root lattices of the finite-dimensional simple Lie algebras of type D-4n and the cosets in their integral duals, in terms of E-4(z) and Delta(24)(z). Using these two identities, we prove that three families of weighted symmetric polynomials of two fixed families of polynomials of E-4(z) and Delta(24)(z) are the theta series of certain positive definite even unimodular lattices, obtained by gluing finitely many copies of the root lattices of the finite-dimensional simple Lie algebras of type D-2n. The results also show that the full permutation groups are the hidden symmetry of the theta series of certain unimodular lattices. |
| 语种 | 英语 |
| WOS记录号 | WOS:000234256600009 |
| 出版者 | WORLD SCIENTIFIC PUBL CO PTE LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/3224]  |
| 专题 | 数学所 |
| 通讯作者 | Xu, XP |
| 作者单位 | Chinese Acad Sci, Acad Math & Syst Sci, Math Inst, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Xu, XP. Theta series of unimodular lattices, combinatorial identities and weighted symmetric polynomials[J]. ALGEBRA COLLOQUIUM,2006,13(1):67-86. |
| APA | Xu, XP.(2006).Theta series of unimodular lattices, combinatorial identities and weighted symmetric polynomials.ALGEBRA COLLOQUIUM,13(1),67-86. |
| MLA | Xu, XP."Theta series of unimodular lattices, combinatorial identities and weighted symmetric polynomials".ALGEBRA COLLOQUIUM 13.1(2006):67-86. |
入库方式： OAI收割
来源：数学与系统科学研究院
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