An intertwining operator for dihedral groups
Robert Donley (New York)
Abstract: In the study of Clebsch-Gordan coefficients for SU(2), Regge observed that the domain space consists of semi-magic squares of size three and that Clebsch-Gordan coefficients transform in accordance with the usual determinant symmetries. These squares are fairly well-understood from a combinatorial viewpoint through permutation matrices. Changing the point of view to representations of finite groups, we use an intertwining operator on dihedral groups for two purposes: to determine the generating function for enumerating points on the corresponding permutation polytopes, and to give a representation theoretic description of a generalization of the algebra of circulant matrices.
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