Weyl group orbits

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Weyl group orbits

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 16 , Issue 1 (March 1990) table of contents

Pages: 94 - 108

Year of Publication: 1990

ISSN:0098-3500

Author

Dennis M. Snow

Univ. of Notre Dame, Notre Dame, IN

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 2, Downloads (12 Months): 34, Citation Count: 1

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ABSTRACT

A new technique is presented for calculating the orbits of the finite Weyl group of a semisimple Lie group G in the weight lattice of G. Such calculations are important in the representation theory of G, and have previously been difficult to carry out for large Weyl groups such as E8. This new technique allows large orbits to be computed using only a small fraction of the computer memory required when using standard techniques. In the case of E8, the memory requirements can be reduced by a factor of 30,000.

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	BOREL, A. Linear Algebraic Groups. Benjamin, New York, 1971.
	2	BOTT, R. Homogeneous vector bundles. Ann. Math. 66 (1957), 203-248.
	3	CARTER, R. Simple Groups of Lie Type. Wiley, New York, 1972.
	4	HUMPHREYS, J. Introduction to Lie Algebras and Representation Theory. Springer Verlag, New York, 1972.
	5	JACOBSON, N. Lie Algebras. Wiley, New York, 1962.
	6	WEYL, H. Theorie der Darstellung der halb-einfacher Gruppen durch lineare Transformationen. Math. Z. 24 (1926), 377-395.