Weyl quantization and a symbol calculus for abelian groups

Journal of the Australian Mathematical Society

N. J. Wildberger¹ 

关键词: primary 44A45 17B05 11F27;   

DOI  :  10.1017/S1446788700008569

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

We develop a notion of a *-product on a general abelian group, establish a Weyl calculus for operators on the group and connect these with the representation theory of an associated Heisenberg group. This can all be viewed as a generalization of the familiar theory for R. A symplectic group is introduced and a connection with the classical Cayley transform is established. Our main application is to finite groups, where consideration of the symbol calculus for the cyclic groups provides an interesting alternative to the usual matrix form for linear transformations. This leads to a new basis for sl(n) and a decomposition of this Lie algebra into a sum of C*artan subalgebras.

【 授权许可】

Unknown