Signature of symmetric rational matrices and the unitary dual of lie groups

Subscribe (Full Service)


	Search: The ACM Digital Library The Guide

	Feedback

Signature of symmetric rational matrices and the unitary dual of lie groups

Full text

Pdf (216 KB)

Source

International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 2005 international symposium on Symbolic and algebraic computation table of contents

Beijing, China

Pages: 13 - 20

Year of Publication: 2005

ISBN:1-59593-095-7

Authors

Jeffrey Adams	University of Maryland, College Park, MD
B. David Saunders	University of Delaware, Newark, DE
Zhendong Wan	University of Delaware, Newark, DE

Sponsors

ACM: Association for Computing Machinery
SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 3, Downloads (12 Months): 20, Citation Count: 1

Additional Information:

abstract references cited by index terms collaborative colleagues

Tools and Actions:	Review this Article Save this Article to a Binder Display Formats: BibTex EndNote ACM Ref

DOI Bookmark:	Use this link to bookmark this Article: http://doi.acm.org/10.1145/1073884.1073889 What is a DOI?

ABSTRACT

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 E8. We conclude that the computation is doable, with a parallel implementation needed for the largest representations.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	J Adams. Integral models of representations of weyl groups. http://atlas.math.umd.edu/weyl/integral.
	2	D. Barbasch. Unitary spherical spectrum for split classical groups, preprint. http://www.math.cornell.edu~barbasch/nsph.ps.
	3	Hervé Brönnimann , Ioannis Z. Emiris , Victor Y. Pan , Sylvain Pion, Sign determination in residue number systems, Theoretical Computer Science, v.210 n.1, p.173-197, Jan. 6, 1999 [doi>10.1016/S0304-3975(98)00101-7 ]
	4	L. Chen, W. Eberly, E. Kaltofen, B. D. Saunders, W. J. Turner, and G. Villard. Efficient matrix preconditioners for black box linear algebra. Linear Algebra and Applications, 343-344:119--146, 2002.
	5	C.Pernet and Z. Wan. LU based algorithms for the characteristic polynomial over a finite field. In Poster, ISSAC'03. ACM Press, 2003.
	6	Jean-Guillaume Dumas, Pascal Giorgi, and Cléement Pernet. FFPACK: Finite field linear algebra package.
	7	Wayne Eberly, Early termination over small fields, Proceedings of the 2003 international symposium on Symbolic and algebraic computation, p.80-87, August 03-06, 2003, Philadelphia, PA, USA [doi>10.1145/860854.860882]
	8	I. Z. Emiris. A complete implementation for computing general dimensional convex hulls. Inter. J. Comput. Geom. Appl., 8:223--253, 1998.
	9	F. R. Gantmacher. The Theory of Matrices. Chelsea, New York, NY, 1959.
	10	G. H. Golub and C. F. Van Loan. Matrix Computations. Johns Hopkins University Press, Baltimore, Maryland, third edition, 1996.
	11	James E. Humphreys. Reflection groups and Coxeter groups, volume 29 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 1990.
	12	E. Kaltofen , A. Lobo, On rank properties of Toeplitz matrices over finite fields, Proceedings of the 1996 international symposium on Symbolic and algebraic computation, p.241-249, July 24-26, 1996, Zurich, Switzerland [doi>10.1145/236869.237081]
	13	Erich Kaltofen , B. David Saunders, On Wiedemann's Method of Solving Sparse Linear Systems, Proceedings of the 9th International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, p.29-38, October 07-11, 1991
	14	Erich Kaltofen, An output-sensitive variant of the baby steps/giant steps determinant algorithm, Proceedings of the 2002 international symposium on Symbolic and algebraic computation, p.138-144, July 07-10, 2002, Lille, France [doi>10.1145/780506.780524]
	15	David Saunders , Zhendong Wan, Smith normal form of dense integer matrices fast algorithms into practice, Proceedings of the 2004 international symposium on Symbolic and algebraic computation, p.274-281, July 04-07, 2004, Santander, Spain [doi>10.1145/1005285.1005325]
	16	John R. Stembridge. Explicit matrices for irreducible representations of Weyl groups. Represent. Theory (electronic), 8:267--289, 2004.
	17	D H Wiedemann, Solving sparse linear equations over finite fields, IEEE Transactions on Information Theory, v.32 n.1, p.54-62, Jan. 1986 [doi>10.1109/TIT.1986.1057137]