Signature of Symmetric Rational Matrices and the Unitary Dual of Lie Groups

机译：对称有理矩阵的签名和李群的Dual对偶

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A key step in the computation of the unitary dual of a Lie group is the determination if certain rational symmetric matrices are positive semi-definite. The size of some of the computations dictates that high performance integer matrix computations be used. We explore the feasibility of this approach by developing three algorithms for integer symmetric matrix signature and studying their performance both asymptotically and experimentally on a particular matrix family constructed from the exceptional Weyl group E_8 We conclude that the computation is doable, with a parallel implementation needed for the largest representations.

机译：李群group对偶计算的关键步骤是确定某些有理对称矩阵是否为正半定矩阵。一些计算的大小决定了要使用高性能整数矩阵计算。我们通过开发三种用于整数对称矩阵签名的算法并在由特殊的Weyl组E_8构造的特定矩阵族上渐近和实验地研究其性能，来探索这种方法的可行性。最大的代表。

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来源
《International Symposium on Symbolic and Algebraic Computation(ISSAC'05); 20050724-27; Beijing(CN)》|2005年|P.13-20|共8页
会议地点 Beijing(CN)
作者
Jeffrey Adams; B. David Saunders; Zhendong Wan;
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作者单位

Department of Mathematics University of Maryland College Park, MD, 20742 USA;

Department of Computer and Information Sciences University of Delaware Newark, DE, 19716 USA;

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会议组织
原文格式 PDF
正文语种 eng
中图分类代数、数论、组合理论;
关键词
matrix signature; symmetric matrix; lie group;

机译：矩阵签名;对称矩阵;李群;

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1. 非光滑数学规划的对称对偶与自身对偶 [J] . 董加礼东北数学：英文版 . 1995,第002期
2. The origin of unequal bond lengths in the (C)over-tilde B-1(2) state of SO2: Signatures of high-lying potential energy surface crossings in the low-lying vibrational structure [J] . Park G. Barratt, Jiang Jun, Field Robert W. The Journal of Chemical Physics . 2016,第14期

机译：SO2在（C）波浪形B-1（2）状态下键长不等的起源：低层振动结构中高位势能面交叉的特征
3. Unitary similarity to a complex symmetric matrix and its extension to orthogonal symmetric Lie algebras [J] . Liu X., Nguelifack B.M., Tam T.-Y. Linear Algebra and its Applications . 2013,第10期

机译：与复对称矩阵的相似性及其对正交对称李代数的扩展
4. Symmetric matrices, orthogonal Lie algebras and Lie-Yamaguti algebras [J] . Benito Pilar, Bremner Murray, Madariaga Sara Linear & Multilinear Algebra: An International Journal Publishing Articles, Reviews and Problems . 2015,第4a6期

机译：对称矩阵，正交李代数和李-亚马古提代数
5. Signature of symmetric rational matrices and the unitary dual of lie groups [C] . Jeffrey Adams, B. David Saunders, Zhendong Wan Proceedings of the 2005 International Symposium on Symbolic and Algebraic Computation(ISSAC'05) . 2005

机译：对称有理矩阵的签名和李群的dual对偶
6. Symmetric singular value decomposition of complex symmetric matrices. [D] . Xu, Wei. 2007

机译：复杂对称矩阵的对称奇异值分解。
7. ON UNITARY REPRESENTATIONS OF NILPOTENT LIE GROUPS [O] . Jacques Dixmier 1957

机译：弱势李群的统一表示
8. The origin of unequal bond lengths in the C̃¹B₂ state of SO₂: Signatures of high-lying potential energy surface crossings in the low-lying vibrational structure [O] . Park, G. Barratt, Jiang, Jun, Field, Robert W. 2016

机译：sO 2的C 1 B 2状态中不等键长的起源：低位振动结构中高位势能面交叉的特征

Signature of Symmetric Rational Matrices and the Unitary Dual of Lie Groups

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