Atypical representations of the Lie superalgebra sl ( 1 , n ) for n greater than 1
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چکیده
(identical representation). The even part G0 is characterized by the condition a0i = ai0 = 0 for i = 1, . . . , n. G0 is isomorphic to gl(n). We choose the Cartan subalgebra H as the set of diagonal matrices of G and G0 resp. Let eij be denote the (n+ 1)× (n+ 1)-matrix with 1 at the place (i, j) and 0 everywhere (i, j = 0, . . . , n) . Then we get by h1 = e00 + e11 , hi = ei−1,i−1 − eii (i = 2, . . . , n) a basis of H . The sets
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