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Isotypic component
The
isotypic
component
of
weight
of a
Lie algebra module
is
the sum
of all
submodules
which are
isomorphic
to the
highest weight module
with weight.
Definition
A
finite-dimensional
module
of a
reductive Lie algebra
can be
decomposed
into
irreducible
submodules
Each finite-dimensional
irreducible representation
of is uniquely
identified
by its
highest weight
In the
decomposition
of, a certain
isomorphism class
might
appear
more than once,
hence
This
defines
the isotypic component of weight of V:
where is maximal.
