Guidelines for the Atlas Web Interface

1. Groups:

Classical groups of rank <= 8
[SL(n,R)  (GL(n) coordinates via coordinates.at) after GL(n)]
GL(n,R)
[SU(p,q)  (same) GL(n)]
U(p,q)
GL(n,H)  
Sp(2n,R)
Sp(p,q)
SO(p,q)
SO^*(2n)
Complex Classical Groups (rank <=8) (as real groups)
[SL(n,C)   coordinates.at]
GL(n,C)
Sp(2n,C)
SO(n,C)

2. Parameters (for irreducible and standard representations)
For each group there are various options to 
choose parameters, not all options apply to all groups
For some there is a choice of infinitesimal character 

Infinitesimal character 
Specify in standard coordinates Q^rank(G)
(not necessarily dominant)

trivial representation 
finite dimensional specified by highest weight or infinitesimal character 
Large discrete series (G equal rank quasisplit)
Holomorphic discrete series (G equal rank Hermitian)
discrete series given by HC parameter (G equal rank)
spherical principal series by infinitesimal character  (G split) (quasisplit?)
large fundamental series (G quasisplit)
all A_q(lambda) with given regular integral infinitesimal character 
all representations with given infinitesimal character   

Specify an arbitrary parameter (?):
Specify real parabolic
M=GL(1,R)^a x GL(2,R)^b x classical
GL(1,R): (epsilon,nu)
GL(2,R): (k,nu)
classical: HC parameter for a discrete series

3. Properties of irreducible representations
Given an irreducible representation information is available about it
infinitesimal character 
lowest K-types, given by highest weights in nice coordinates for 
G(R) connected (what precisely in the disconnected case?: plus/minus only)
branching up to given level
character formula
is_unitary (fast algorithm at regular integral infinitesimal character: test if an A_q(lamba)
otherwise is_unitary in equal rank case, unequal rank case will be done soon (I insist)
[Weakly fair range?]
cuspidal data
theta-stable data
integral root system 
tau invariant

4. Properites of standard representations
specified by a parameter
infinitesimal character 
composition series
lowest K-types and branching as for irreducible representations
Jantzen filtration