Let n = n1 + ⋯ + nr, where
r ≧ 2 and the ni′s are positive integers. Then every element of G = SL(n,C) can be
written as a block matrix (gij)1≦i,j≦r, where each block gij is a ni × nj matrix. Let
Gn1,…,nr denote the subgroup of all diagonal block matrices, i.e., gij is the 0-matrix
for i≠j. Let Tx be any element of the non-degenerate principal series of G. The main
purpose of this paper is to decompose the restriction of Tx to Gn1,…,nr into
irreducible representations.
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