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Abstract
Supercharacter theory is developed by P. Diaconis and I. M. Isaacs as a natural generalization of the classical ordinary character theory. Some classical sums of number theory appear as supercharacters which are obtained by the action of certain subgroups of GL_d(Z_n) on Z_n^d. In this paper we take Z_p^d, p prime, and by the action of certain subgroups of GL_d(Z_p) we find supercharacter table of Z_p^d.
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References
- Andre, C.A.M., Basic characters of the unitriangular group,J. Alg., 175 (1995) 287-319.
- Brumbaugh, J.L., et al. , Supercharacters, exponential sums, and the uncertainly principle, J. Number theory, 144 (2014), 151-175.
- Diaconis, P., and Isaacs, I.M., Supercharacters and superclasses for algebra groups, Trans. Amer. Math. Soc., 360:5 (2008), 2359-2392.
- Dornhoff, L., Group representation theory, Part A, ordinary representation theory, Marcel Dekker, Inc. New York, 1971.
- Isaacs, I.M., Character theory of finite groups, Dover, New York, 1994.
- Hendrikson, A.O.F., Supercharacter theory constructions corresponding to Schur ring products, Comm. Alg., 40 (2012), 4420-4438.
- Hendrikson, A.O.F., Supercharacter theories of finite cyclic groups, Ph.D. dissertation, University of Wisconsin Madison, 2008
References
Andre, C.A.M., Basic characters of the unitriangular group,J. Alg., 175 (1995) 287-319.
Brumbaugh, J.L., et al. , Supercharacters, exponential sums, and the uncertainly principle, J. Number theory, 144 (2014), 151-175.
Diaconis, P., and Isaacs, I.M., Supercharacters and superclasses for algebra groups, Trans. Amer. Math. Soc., 360:5 (2008), 2359-2392.
Dornhoff, L., Group representation theory, Part A, ordinary representation theory, Marcel Dekker, Inc. New York, 1971.
Isaacs, I.M., Character theory of finite groups, Dover, New York, 1994.
Hendrikson, A.O.F., Supercharacter theory constructions corresponding to Schur ring products, Comm. Alg., 40 (2012), 4420-4438.
Hendrikson, A.O.F., Supercharacter theories of finite cyclic groups, Ph.D. dissertation, University of Wisconsin Madison, 2008