Vol. 38, No. 2, 1971

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Restriction of the principal series of SL(n, C) to some reductive subgroups

Nguyen Huu Anh

Vol. 38 (1971), No. 2, 295–314
Abstract

Let n = n1 + + nr, where r 2 and the nis are positive integers. Then every element of G = SL(n,C) can be written as a block matrix (gij)1i,jr, 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 ij. 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.

Mathematical Subject Classification 2000
Primary: 22E45
Milestones
Received: 5 August 1970
Published: 1 August 1971
Authors
Nguyen Huu Anh