# Kazhdan-Lusztig polynomials for the block of the trivial representation
# of Sp(4,R) and its dual block for SO(3,2)

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#First Sp(4,R)

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

block: klbasis
Name an output file (hit return for stdout):
Full list of non-zero Kazhdan-Lusztig-Vogan polynomials:

 0:  0: 1

 1:  1: 1

 2:  2: 1

 3:  3: 1

 4:  0: 1
     2: 1
     4: 1

 5:  1: 1
     3: 1
     5: 1

 6:  0: 1
     1: 1
     6: 1

 7:  0: 1
     1: 1
     2: 1
     3: 1
     4: 1
     5: 1
     6: 1
     7: 1

 8:  0: 1
     1: 1
     2: 1
     4: 1
     6: 1
     8: 1

 9:  0: 1
     1: 1
     3: 1
     5: 1
     6: 1
     9: 1

10:  0: 1
     1: 1
     2: 1
     3: 1
     4: 1
     5: 1
     6: 1
     7: 1
     8: 1
     9: 1
    10: 1

11:  2: q
     3: q
     7: 1
    11: 1

48 nonzero polynomials, and 5 zero polynomials,
 at 53 Bruhat-comparable pairs.

# Now the dual block of SO(3,2)

block: 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 (return for stdout, ? to abandon):
entering block construction... K\G/B and dual generated... done
 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
block: klbasis
Name an output file (return for stdout, ? to abandon):
Full list of non-zero Kazhdan-Lusztig-Vogan polynomials:

 0:  0: 1

 1:  1: 1

 2:  0: 1
     1: 1
     2: 1

 3:  0: 1
     3: 1

 4:  0: 1
     4: 1

 5:  0: 1
     1: 1
     2: 1
     3: 1
     5: 1

 6:  0: 1
     1: 1
     2: 1
     4: 1
     6: 1

 7:  0: 2
     1: 1
     2: 1
     3: 1
     4: 1
     7: 1

 8:  0: 1
     1: 1
     2: 1
     3: 1
     5: 1
     7: 1
     8: 1

 9:  0: 1
     1: 1
     2: 1
     4: 1
     6: 1
     7: 1
     9: 1

10:  1: q
     5: 1
    10: 1

11:  1: q
     6: 1
    11: 1

45 nonzero polynomials, and 8 zero polynomials,
 at 53 Bruhat-comparable pairs.