SchurRing -- the class of all Schur rings

SchurRing -- the class of all Schur rings

The type SchurRing is a member of the class Type. Each object of class SchurRing is called a Schur ring. Each Schur ring is also a member of class EngineRing.

More general types (whose methods may also apply) :

EngineRing -- the class of rings handled by the engine

Ring -- the class of all rings

Type -- the class of all types

MutableHashTable -- the class of all mutable hash tables

HashTable -- the class of all hash tables

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

See also:

SchurRing -- the class of all Schur rings

List -- the class of all lists -- {...}

Functions and methods returning a a Schur ring :

Schur ZZ

Methods for using a Schur ring :

SchurRing _ {...} -- make an element of a Schur ring

toString SchurRing