####################################################################
#  Compute select products in the K-theory rings of                #
#  OG(8,16) and LG(7,14).                                          #
#  This reproduces Example 4.9 and Example 5.8 in the paper        #
#  "Pieri rules for the K-theory of cominuscule Grassmannians"     #
#  by A. Buch and V. Ravikumar.                                    #
####################################################################


read equivcalc:
with(equivcalc):


la := X[6,4,1]:
mu := X[5]:
nu := X[7,6,3,1]:


printf("K(OG(8,16)):\n"):
OG(8,16):
u := part_weyl(la):
v := part_weyl(mu):
w := part_weyl(nu):
prd := kmult(u, v):
lprint(weyl_part(u * v = prd)):
printf("Coefficient of %a: %d\n", nu, coeff(prd, w)):
printf("\n");


printf("K(LG(7,14)):\n"):
SG(7,14):
u := part_weyl(la):
v := part_weyl(mu):
w := part_weyl(nu):
prd := kmult(u, v):
lprint(weyl_part(u * v = prd)):
printf("Coefficient of %a: %d\n", nu, coeff(prd, w)):


###
