Irreducible Representations of Algebraic Group SL(6,K) in charK =3

Abstract

For each irreducible module Xi Nanhua defined an element which generated this module. We use this element to construct a certain basis for and then compute dim , determine its formal characters in this paper. In order to obtain faster speed we modify the algorithm to compute the irreducible characters.

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Zhou, Z. (2014) Irreducible Representations of Algebraic Group SL(6,K) in charK =3. Advances in Pure Mathematics, 4, 535-544. doi: 10.4236/apm.2014.410062.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Gilkey, P.B. and Seitz, G.M. (1988) Some Representations of Exceptional Lie Algebras. Geometriae Dedicata, 25, 407-416. http://dx.doi.org/10.1007/BF00191935
[2] Dowd, M. and Sin, P. (1996) On Representations of Algebraic Groups in Characteristic Two. Communications in Algebra, 24, 2597-2686. http://dx.doi.org/10.1007/BF00191935
[3] http://pi.math.virginia.edu/~lls2l/research_undergrad.htm
[4] http://math.rutgers.edu/~asbuch/dynkin/
[5] Lusztig, G. (1993) Introduction to Quantum Groups. Progress in Mathematics, 110, Birkháuser.
[6] Xi, N.H. (1996) Irreducible Modules of Quantized Enveloping Algebras at Roots of 1. Publ. RIMS, Kyoto Univ, 32, 235-276. http://dx.doi.org/10.2977/prims/1195162964
[7] Xu, B.X. and Ye, J.C. (1997) Irreducible Characters of Algebraic Groups in Characteristic Two (I). Algebra Colloquium, 4, 281-290.
[8] Ye, J.C. and Zhou, Z.G. (2000) Irreducible Characters of Algebraic Groups in Characteristic Two (III). Communications in Algebra, 28, 4227-4247. http://dx.doi.org/10.1080/00927870008827086
[9] Ye, J.C. and Zhou, Z.G. (2001) Irreducible Characters for Algebraic Groups in Characteristic Three. Communications in Algebra, 29, 201-223. http://dx.doi.org/10.1081/AGB-100000795
[10] Ye, J.C. and Zhou, Z.G. (2002) Irreducible Characters for Algebraic Groups in characteristic Three (II). Communications in Algebra, 30, 273-306. http://dx.doi.org/10.1081/AGB-120006491
[11] Jantzen, J.C. (1987) Representations of Algebraic Groups. Academic Press, Orlando.
[12] Andersen, H.H. (1980) The Strong Linkage Principle. Journal fur die Reine und Angewandte Mathematik, 315, 53-59.

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