Dimensions of the simple restricted modules for the restricted contact Lie algebra (Q1340439)

The author computes the dimensions of the simple restricted modules of the restricted contact Lie algebra \(K_ n\) corresponding to exceptional weights. In a previous paper [Am. Math. Soc. 116, 329-337 (1992; Zbl 0761.17019)], he has shown that in the nonexceptional cases the simple restricted modules are modules induced from simple restricted modules of the homogeneous component of degree zero of \(K_ n\) (which is isomorphic to \(csp (n-1)\)) and hence their dimensions can be calculated in terms of the dimensions of the simple restricted modules of \(sp (n-1)\). The dual relations between the simple restricted modules of \(K_ n\) are also clarified.