The symmetries of the fine gradings of sl(n{sup k},C) associated with direct product of Pauli groups
- Department of Mathematics, College of Science, Zhejiang University, Hangzhou 310027 (China)
A grading of a Lie algebra is called fine if it could not be further refined. For a fine grading of a simple Lie algebra, we define its Weyl group to describe the symmetry of this grading. It is already known that the Weyl group of the fine grading of sl(n,C) induced by the action of the group {Pi}{sub n} of the generalized Pauli matrices of rank n is SL(2,Z{sub n}), where Z{sub n} is the cyclic group of order n. In this paper, we consider the fine grading of sl(n{sup k},C) induced by the action of the group of k-fold tensor product of the generalized Pauli matrices of rank n. We prove that its Weyl group is Sp(2k,Z{sub n}) and is generated by transvections; therefore, this generalizes the previous result.
- OSTI ID:
- 21476483
- Journal Information:
- Journal of Mathematical Physics, Vol. 51, Issue 9; Other Information: DOI: 10.1063/1.3492830; (c) 2010 American Institute of Physics; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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