Weight vector

v

μ \in t^{*}

when

h v = μ (h) v

for every

h

in the Cartan subalgebra.

Table of contents

Weight of a representation

A weight of a representation is a functional

μ

whose weight space is nonzero.

Weight space ( $V_{μ}$ )

The weight space

V_{μ}

consists of all weight vectors of weight

μ

, together with zero.

Weight multiplicity

The multiplicity of a weight

μ

is the dimension of its weight space.

Singular vector

A singular vector is a nonzero weight vector annihilated by the positive nilpotent subalgebra

n^{+}

.

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