Vol. 101, No. 2, 1982

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Fixed points on flag manifolds

Henry H. Glover and William Duncan Homer, II

Vol. 101 (1982), No. 2, 303–306

When K is R, C or H, let UK(n) denote the group of n × n orthogonal, unitary, or symplectic matrices, respectively. If G is a closed connected subgroup of UK(n) of maximal rank, then it is conjugate to a subgroup of the form UK(n1) × UK(n2) × × UK(nk). A simple condition on the integers ni is shown to be necessary for UK(n)∕G to have the fixed point property (that every self map has a fixed point). It is conjectured that this condition is also sufficient, and a proof is given for some cases.

Mathematical Subject Classification 2000
Primary: 55M20
Secondary: 14M17, 54H25
Received: 22 May 1981
Revised: 29 July 1981
Published: 1 August 1982
Henry H. Glover
Department of Mathematics
Ohio State University
Columbus OH 43210-1174
United States
William Duncan Homer, II