SchurRing

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 Schur.

     i1 = R = Schur 4
     
     o1 = R
     
     o1 : SchurRing

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

     i2 = R_{3,2,1}
     
     o2 = {3, 2, 1}
     
     o2 : R

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

     i3 = dim R_{3,2,1}
     
     o3 = 64

Multiplication in the ring comes from tensor product of representations.

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