SchurRing -- the class of all Schur rings

A Schur ring is the representation ring for the general linear group of n by n matrices, and one can be constructed with schurRing.

i1 : R = schurRing(s, 4) o1 = R o1 : SchurRing

The element corresponding to the Young diagram {3,2,1} is obtained as follows.

i2 : s_{3,2,1} o2 = s 3,2,1 o2 : R

The dimension of the underlying virtual representation can be obtained with dim.

i3 : dim s_{3,2,1} o3 = 64

Multiplication in the ring comes from tensor product of representations.

i4 : s_{3,2,1} * s_{1,1} o4 = s + s + s + s + s + s 4,3,1 4,2,2 4,2,1,1 3,3,2 3,3,1,1 3,2,2,1 o4 : R