This note tells (1) how SU(n) particle multiplets are identified or labeled,(2) how to find the number of particles in a multiplet from its label,(3) how to draw the Young diagram for a multiplet,and (4) how to use Young diagrams to determine the overall multiplet structure of a composite system,such as a 3-quark or a meson-baryon system.
In much of the literature,the word "representation" is used where we use "multiplet," and "tableau" is used where we use "diagram."