Maple programs for computing discrete series multiplicities

More specifically, this is for branching from a connected
semisimple real Lie group G to a maximal compact subgroup K.
Blattner's formula (in principle) describes the multiplicities.

John Stembridge
24 June 2005

FILES:
coxeter2.4v.txt  - the coxeter package
blatt            - basic code for computing multiplicities recursively
coneslice        - generate slices of the semigroup generated by the
                   (positive) non-compact roots
prep_work        - generate global structures used by the other programs
dseries          - the main program for computing discrete series

USAGE:
Save these files into a local directory,
launch a maple session,
run the command  "read dseries;"
and start computing.
Read the (scant) documentation in the dseries file.

EXAMPLE:
Compute the discrete series indexed by the sum of the first two
fundamental weights of F4, up to height 5 beyond the height of
the first term of the series, relative to the K determined by
declaring simple roots 2 and 3 to be non-compact (not in K).
(This particular K has root system A1*C3.)

> read dseries;

> diagram(F4);
 
   1---2=<=3---4
 
> w:=weights(F4):
> discrete_series(w[1]+w[2], 5, [2,3], F4);

   1   1     1   0.00   0 [0, 0, 0, 0]
   2   1     2   0.00   1 [0, 1, 0, 0]
   3   1     3   0.00   2 [0, 0, 1, 1]
   4   1     3   0.01   2 [1, 1, 0, 0]
   5   0     5   0.00   3 [0, 0, 2, 1]
   6   1     6   0.00   3 [0, 1, 1, 1]
   7   1     5   0.00   3 [1, 2, 0, 0]
   8   0    10   0.01   4 [0, 1, 2, 1]
   9   0     7   0.00   4 [1, 3, 0, 0]
  10   1     9   0.00   4 [1, 1, 1, 1]
  11   1     6   0.00   4 [2, 2, 0, 0]
  12   1     6   0.00   4 [0, 0, 2, 2]
  13   0    15   0.00   5 [1, 1, 2, 1]
  14   0     9   0.00   5 [0, 0, 3, 2]
  15   2    15   0.01   5 [1, 2, 1, 1]
  16   1     9   0.00   5 [2, 3, 0, 0]
  17   1    12   0.01   5 [0, 1, 2, 2]

                               A1 C3, 17, 0.050

Column #2 lists the multiplicities. For an explanation of
the other columns, see the dseries file.