ISSN:
1572-9486
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract All independent Casimir operatorsK 2j , 1 ≦j ≦n, are considered for the Schurean ∞ -dimensional representations ofosp(1, 2n),n= 1,2, that were constructed recently. For these representations (which are expressed in terms of tensor products of linear differential operators andN byN matrices belonging to a finite set and depending on a real parameterχ) a method is presented by which the “differential-operator part” of operators K2j is effectively eliminated and expressions for K2j via matrices in are obtained. In the same way we treat the Casimir operators Ĉ2j of the even subalgebra sp(2n, ℝ) ⊂osp(1, 2n). The eigenvalues of K2j and Ĉ2j are evaluated as functions of the parameterχ for the representations of osp(1, 2) withN= 2 and ofosp(1, 4) withN = 2, 4.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01597763
