APM  Vol.4 No.10 , October 2014
Irreducible Representations of Algebraic Group SL(6,K) in charK =3
Author(s) Zhongguo Zhou*
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.

Cite this paper
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.
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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