논문KCI 등재
GROBNER-SHIRSHOV BASES FOR IRREDUCIBLE sp₄-MODULES
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We give an explicit construction of Grobner–Shirshov pairs and monomial bases for finite-dimensional irreducible representations of the simple Lie algebra sp₄. We also identify the monomial basis consisting of the reduced monomials with a set of semistandard tableaux of a given shape, on which we give a colored oriented graph structure.
Abstract
We give an explicit construction of Grobner–Shirshov pairs and monomial bases for finite-dimensional irreducible representations of the simple Lie algebra sp₄. We also identify the monomial basis consisting of the reduced monomials with a set of semistandard tableaux of a given shape, on which we give a colored oriented graph structure.
참고문헌 (15)
- L. A. Bokut, "Grobner–Shirshov bases for Lie superalgebras and their universal enveloping algebras", Journal of Algebra, 217(2), pp.461~495 (1999)
- L. A. Bokut, "Serre relations and Gr¨obner–Shirshov bases for simple Lie algebras I,II", International Journal of Algebra and Computation, 6(4), pp.389~400 (1996)
- L. A. Bokut, "Grobner–Shirshov bases for exceptional Lie algebras I", Journal of Pure and Applied Algebra, 133(1), pp.51~57 (1998)
- L. A. Bokut, "Gr¨obner–Shirshov bases for exceptional Lie algebras E6;E7;E8, in “Algebra and combinatorics (Hong Kong, 1997)”", pp.37~46 (1999), Springer-Verlag
- B. Buchberger, "An algorithm for finding a basis for the residue class ring of a zerodimensional ideal", 박사, pp.1965
- J. Hong, "Introduction to Quantum Groups and Crystal Bases, Graduate Studies in Mathematics", pp.42~ (2002), American Mathematical Society
- J. E. Humphreys, "Introduction to Lie Algebras and Representation Theory, Graduate Texts in Mathematics, Vol. 9" (1972), Springer-Verlag
- V. G. Kac, "Infinite-dimensional Lie Algebras" (1990), Cambridge University Press
- S.-J. Kang, "Linear algebraic approach to Gr¨obner– Shirshov basis theory", Journal of Algebra, 313(2), pp.988~1004 (2007)
- S.-J. Kang, "Hecke algebras, Specht modules and Gr¨obner–Shirshov bases", Journal of Algebra, 252(2), pp.258~292 (2002)
- S.-J. Kang, "Representations of Ariki-Koike algebras and Grobner–Shirshov bases", Proc. London Math. Soc., 통권 : 89, pp.54~70 (2004)
- S.-J. Kang, "Grobner–Shirshov bases for representation theory", Journal of the Korean Mathematical Society, 37(1), pp.55~72 (2000)
- S.-J. Kang, "Grobner–Shirshov bases for irreducible sln+1-modules", Journal of Algebra, 232(1), pp.1~20 (2000)
- P. Lalonde, "Standard Lyndon bases of Lie algebras and enveloping algebras", Transactions of the American Mathematical Society, 347(5), pp.1821~1830 (1995)
- A. I. Shirshov, "Some algorithm problems for Lie algebras", Sibirsk Matematica, 3, pp.292~296 (1962)
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