This is the Atlas of Reductive Lie Groups Software Package version 0.3. Enter "help" if you need assistance. # First the block of the trivial representation of Sp(4,R) # (split, rank 2, 4x4 matrices) # There are 2 principal series and 4 discrete series empty: type Lie type: C2 sc s main: block (weak) real forms are: 0: sp(2) 1: sp(1,1) 2: sp(4,R) enter your choice: 2 possible (weak) dual real forms are: 0: so(5) 1: so(4,1) 2: so(2,3) enter your choice: 2 Name an output file (hit return for stdout): 0( 0,6): 0 0 [i1,i1] 1 2 ( 6, *) ( 4, *) 1( 1,6): 0 0 [i1,i1] 0 3 ( 6, *) ( 5, *) 2( 2,6): 0 0 [ic,i1] 2 0 ( *, *) ( 4, *) 3( 3,6): 0 0 [ic,i1] 3 1 ( *, *) ( 5, *) 4( 4,4): 1 2 [C+,r1] 8 4 ( *, *) ( 0, 2) 2 5( 5,4): 1 2 [C+,r1] 9 5 ( *, *) ( 1, 3) 2 6( 6,5): 1 1 [r1,C+] 6 7 ( 0, 1) ( *, *) 1 7( 7,2): 2 1 [i2,C-] 7 6 (10,11) ( *, *) 2,1,2 8( 8,3): 2 2 [C-,i1] 4 9 ( *, *) (10, *) 1,2,1 9( 9,3): 2 2 [C-,i1] 5 8 ( *, *) (10, *) 1,2,1 10(10,0): 3 3 [r2,r1] 11 10 ( 7, *) ( 8, 9) 1,2,1,2 11(10,1): 3 3 [r2,rn] 10 11 ( 7, *) ( *, *) 1,2,1,2 # now its dual block of SO(3,2) (adjoint) # There are 4 principal series and 2 discrete series real: type Lie type: B2 ad s main: block (weak) real forms are: 0: so(5) 1: so(4,1) 2: so(2,3) enter your choice: 2 possible (weak) dual real forms are: 0: sp(2) 1: sp(1,1) 2: sp(4,R) enter your choice: 2 Name an output file (hit return for stdout): 0(0,10): 0 0 [i1,i2] 1 0 ( 2, *) ( 3, 4) 1(1,10): 0 0 [i1,ic] 0 1 ( 2, *) ( *, *) 2(2, 7): 1 2 [r1,C+] 2 7 ( 0, 1) ( *, *) 1 3(3, 8): 1 1 [C+,r2] 5 4 ( *, *) ( 0, *) 2 4(3, 9): 1 1 [C+,r2] 6 3 ( *, *) ( 0, *) 2 5(4, 4): 2 1 [C-,i2] 3 5 ( *, *) ( 8,10) 1,2,1 6(4, 5): 2 1 [C-,i2] 4 6 ( *, *) ( 9,11) 1,2,1 7(5, 6): 2 2 [i2,C-] 7 2 ( 8, 9) ( *, *) 2,1,2 8(6, 0): 3 3 [r2,r2] 9 10 ( 7, *) ( 5, *) 2,1,2,1 9(6, 1): 3 3 [r2,r2] 8 11 ( 7, *) ( 6, *) 2,1,2,1 10(6, 2): 3 3 [rn,r2] 10 8 ( *, *) ( 5, *) 2,1,2,1 11(6, 3): 3 3 [rn,r2] 11 9 ( *, *) ( 6, *) 2,1,2,1