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Grobner-Shirshov bases for representation theory

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Authors
Kang, Seok-Jin; Lee, Kyu-Hwan
Issue Date
2000
Publisher
대한수학회 = The Korean Mathematical Society
Citation
J. Korean Math. Soc. 37 (2000), 55-72
Keywords
Gr6bner-Shirshov pairmonomial basisrepresentationsimple Lie algebrasemistandard Young tableau
Abstract
In this paper, we develop the Gr6bner-Shirshov basis
theory for the representations of associative algebras by introducing
the notion of Gr6bner-Shirshov pairs. Our result can be applied to
solve the reduction problem in representation theory and to construct
monomial bases of representations of associative algebras. As
an illustration, we give an explicit construction of Gr6bner-Shirshov
pairs and monomial bases for finite dimensional ir:-educible representations
of the simple Lie algebra Sl3' Each of these monomial
bases is in 1-1 corr3spondence with the set of semistandard Young
tableaux with a given shape.
ISSN
0304 - 9914
Language
English
URI
http://hdl.handle.net/10371/12179
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College of Natural Sciences (자연과학대학)Dept. of Mathematical Sciences (수리과학부)Journal Papers (저널논문_수리과학부)
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