# Group-to-representation map

From Groupprops

This term is related to: linear representation theory

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## Definition

Let be a finite group and a field that is sufficiently large for . A **group-to-representation map** is an expression of as a disjoint union:

where varies over the irreducible representations of , and is a set whose size is the degree of .

## Properties

We call the group-to-representation map self-adjoint if and correspond to the same and are simply the same thing with the coordinates flipped.

## Example

The RSK-correspondence gives an example of a group-to-representation map when the group in question is a symmetric group.