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

Nguyen Huu Anh

Vol. 38 (1971), No. 2, 295–314

DOI: 10.2140/pjm.1971.38.295

Abstract

Let n = n₁ + ⋯ + n_r, where r ≧ 2 and the n_i′s are positive integers. Then every element of G = SL(n,C) can be written as a block matrix (g_ij)_1≦i,j≦r, where each block g_ij is a n_i × n_j matrix. Let G_n1,…,nr denote the subgroup of all diagonal block matrices, i.e., g_ij is the 0-matrix for i≠j. Let T^x be any element of the non-degenerate principal series of G. The main purpose of this paper is to decompose the restriction of T^x to G_n1,…,nr into irreducible representations.

Mathematical Subject Classification 2000

Primary: 22E45

Milestones

Received: 5 August 1970

Published: 1 August 1971