My function that I have written to compute the rank of fundamental representations is as follows:
# given a prime p, return all A_n representations of dimension = p^2
def rankrep(p):
bound = p*p
s = SymmetricFunctions(QQ).schur()
Sym_p = s[p]
A = lambda i: WeylCharacterRing("A{0}".format(i))
deg = []
index = []
L = []
for i in xrange(bound):
deg.append([])
fw = A(i+1).fundamental_weights()
temp = A(i+1)
for j in fw.keys():
deg[i].append(temp(fw[j]).degree())
if temp(fw[j]).degree() == bound:
index.append('A'+str(i+1)+'(fw['+str(j)+'])')
L.append(fw[j])
return index, deg
But now if I call rankrep it does not let me store index or deg, it just prints them. I am wanting to also store the L variable I create as these are the weights that give me the desired dimension, and convert from these weights, which make up the highest weight $Lambda = a_1 \omega_1 + \cdots + a_n \omega_n$ (here $Lambda$ is the high weight, $\omega_i$ are the fundamental weights). The $\omega_i$ have the form $(1,1,\dots,1,0, \dots, 0)$, and I would like to express my high weight as $(a_1 + \cdots + a_{n-1}, a_2 + \cdots + a_{n-1}, \dots, a_{n-1},0)$. However, since I am only considering one of the $a_i$ nonzero, this vector will look like $(a_i, a_i, \dots, a_i, 0, \dots, 0)$. I would like to store this vector, and then pass it as a partition to a schur function s that I define in the code.
How can I store these outputs and format them (i.e., data types, lists, dictionaries, vectors) so that I can then alter them as described and apply my schur function?
