nci_nilrad_roots.at

all_sums

given a set S of N ratvecs all of length n
returns all 2^N sums of vectors in subsets of S
caution: if S is empty this returns [ratvec:[]]
  i.e. the list of 1 ratvec of length 0
  (rather than [ratvec]:[] the empty list of ratvecs, which has length 0)
  this is appropriate since the expected length of the list is 2^N=2^0=1
otherwise =[null(n),...]

sums_of_size_k

given a set S of N ratvecs all of length n
return list of sums in all subsets of size k

makeS

like makeS in induction.at, except only keep the roots in u

also defined in parabolics.at, induction.at

nci_nilrad_roots_restricted_to_H_theta

Given a theta-stable parabolic P and x_G\in KGB(G)
 return a set of nci roots of H, whose restrictions to H^{theta_x} are
 the weights of H^theta on u\cap s
 each nci root contributes itself
 each pair of complex roots for G contributes one of them
Note: our application will be to L_0\subset L\subset G
 q=l+u is the parabolic, we're interested in tensoring L_0\cap K-types
 for this command all that matters is \theta_x restricted to H
 so L_0 plays no role

Dangerous bend: this is a KGBElt for L (what is needed for a weight function to compute
tensor products) but the roots are for G, so embed_KGB(x_L,G)

also in this file at line 53

nci_nilrad_roots_restricted_to_H_theta

returns a function taking a KGBElt to [ratvec]

also in this file at line 41

sums_nci_nilrad_roots_wedge_k_restricted_to_H_theta

first compute the previous function to give a set of n roots
run over the binom(n,k) subsets of size k of this set, and return their sums

sums_nci_nilrad_roots_restricted_to_H_theta

first compute the ante-previous function to give a set of n roots
run over the 2^n subsets of this set, and return their sums