plethysm(BasicList,RingElement) -- Plethystic operations on representations

Synopsis

Usage:
pl = plethysm(lambda,g)
Function: plethysm
Inputs:
- lambda, a basic list, nonincreasing sequence of positive integers, or partition
- g, a ring element, element of Symmetric ring or Schur ring
Outputs:
- pl, a ring element, element of the ring of g

Description

The method computes the character of the representation obtained by applying the Schur functor S_λ to the representation with character g, where λ is a partition.

R = symmetricRing(QQ,3);

S = schurRing(QQ,q,3);

toE plethysm({2,1},e_1*e_2-e_3)

plethysm({2,1,1},q_{1,1})

T = schurRing(S,t,4,GroupActing => "Sn");

plethysm({1,1},q_1*t_{3,1})