14 ELDAR STRAUME

Remarks 1.5 (a) A classification of compact connected maximal linear groups of

cohomogeneity 2 or 3 first appeared in [HL], but some cases were overlooked, some of

which were later described in [U]. However, two maximal groups were still missing,

namely the following two types with c(O) = 3 (cf. #20 and #23, Table III) :

(i) (G,D) = (Sp(1) x Sp(n),s3

V l

% v

n

), n 1,

(ii) (U(2) xSp(n),[|i2 ®LVn]|R), n 1.

(b) Consider a reducible group (G,0), 0 = 0^ + • + £[, k = 2, 3. If c(I) = 2,

and hence k = 2 and c(Oj) = 1, then the corresponding maximal connected group is the

splitting group (SO(n-|),p

ni

) © (SO(n2),Pno)' n i = dlm[R ° i - l n a s i m i l a r w a Y if

c(D) = 3 and either k = 3, or k = 2 and c(Oj) = i, then the corresponding maximal

group is splitting (and hence is not in our tables).