Fine grading of sl(p, C) generated by tensor product of generalized Pauli matrices and its symmetries
نویسندگان
چکیده
Study of the normalizer of the MAD-group corresponding to a fine grading offers the most important tool for describing symmetries in the system of non-linear equations connected with contraction of a Lie algebra. One fine grading that is always present in any Lie algebra sl(n, C) is the Pauli grading. The MAD-group corresponding to it is generated by generalized Pauli matrices. For such MAD-group, we already know its normalizer; its quotient group is isomorphic to the Lie group SL(2, Zn)× Z2. In this paper, we deal with a more complicated situation, namely that the fine grading of sl(p, C) is given by a tensor product of the Pauli matrices of the same order p, p being a prime. We describe the normalizer of the corresponding MAD-group and we show that its quotient group is isomorphic to Sp(4, Fp)× Z2, where Fp is the finite field with p elements.
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