bott(List,ZZ,ZZ) -- cohomology table of Schur functor of tautological bundle on P^n

Synopsis

Function: bott
Usage:

bott(L,lowDegree,highDegree)
Inputs:
- L, a list, a non-increasing sequence of integers
- lowDegree, an integer
- highDegree, an integer
Outputs:
- a Cohomology tally

Description

Produces a CohomologyTally of the vector bundle S_L(Q), between the column whose index is lowDegree and the column whose index is highDegree. See bott(List,ZZ) for the definition of Q.

i1 : C1 = bott({3,2,1},-10,10)

        -10  -9  -8  -7  -6 -5 -4 -3 -2 -1  0   1   2   3   4   5    6    7    8    9   10
o1 = 3: 924 640 420 256 140 64 20  .  .  .  .   .   .   .   .   .    .    .    .    .    .
     2:   .   .   .   .   .  .  .  4  .  .  .   .   .   .   .   .    .    .    .    .    .
     1:   .   .   .   .   .  .  .  .  4  .  .   .   .   .   .   .    .    .    .    .    .
     0:   .   .   .   .   .  .  .  .  . 20 64 140 256 420 640 924 1280 1716 2240 2860 3584

o1 : CohomologyTally

i2 : C2 = pureCohomologyTable({-2,-4,-6},-10,10) 

        -10  -9  -8 -7 -6 -5 -4 -3 -2 -1  0  1  2   3   4   5   6   7   8   9  10
o2 = 3: 231 160 105 64 35 16  5  .  .  .  .  .  .   .   .   .   .   .   .   .   .
     2:   .   .   .  .  .  .  .  1  .  .  .  .  .   .   .   .   .   .   .   .   .
     1:   .   .   .  .  .  .  .  .  1  .  .  .  .   .   .   .   .   .   .   .   .
     0:   .   .   .  .  .  .  .  .  .  5 16 35 64 105 160 231 320 429 560 715 896

o2 : CohomologyTally

i3 : C1 == 4 * C2

o3 = true

Ways to use this method: