The "blocku" command lists all the elements of the current block of
representations that are unitary at infinitesimal character rho.
These are precisely Zuckerman's "A_q" representations attached to
theta-stable parabolic subalgebras q.
The output is mostly a subset of the output of the "block" command. Each row
of the output corresponds to a single unitary representation. The first
column is the number of the representation in the block, followed by the $x$
and $y$ coordinates for the element as in the block command. The next two
columns give the length of the parameter, and the number of its Cartan class.
The next r columns (where r is the number of simple roots) describe
the descent status of the simple roots. Possible entries for the
simple root alpha are as follows (with theta the Cartan involution):
i1: alpha is imaginary type I noncompact (meaning that $s_\alpha$ is not
in the real Weyl group)
i2: alpha is imaginary type II noncompact (meaning that $s_\alpha$ is in
the real Weyl group)
ic: alpha is imaginary compact
C+: alpha is complex, and theta(alpha) is positive.
C-: alpha is complex, and theta(alpha) is negative.
r2: alpha is a type II real root (meaning that alpha takes the value
-1 on the real Cartan)
r1: alpha is a type I real root (meaning that alpha does not take the
value -1)
(Non-parity real roots rn cannot appear for an A_q representation.)
The next r columns give the descent status of the simple roots in the
Levi subalgebra $l$ of $q$; roots not in $l$ are indicated with an
asterisk. Because the representation is trivial on $l$, the only
possible entries in these columns are r1, r2, C-, and *.
The final column describes a sequence of cross actions and Cayley transform
reaching this representation from an irreducible fundamental series, as is
described in the help for "blockd". The number of such steps is the length of
the representation.