# Layer structure of irreducible Lie algebra modules

Let h be a Cartan subalgebra of the finite-dimensional simple complex Lie algebra g. It is argued that every finite-dimensional irreducible g-module admits a unique vector-space decomposition in terms of layers, where a layer is an h-module associated with the set of distinct weights appearing in an irreducible g-module. Ensuing results include a new approach to the computation of Weyl characters, and a closed-form expression for the number of distinct weights in a finite-dimensional irreducible g-module. The latter is given by a polynomial in the Dynkin labels, of degree given by the rank of g

### About Pure mathematics seminars

We present regular seminars on a range of pure mathematics interests. Students, staff and visitors to UQ are welcome to attend, and to suggest speakers and topics.

Seminars are usually held on Tuesdays from 3pm to 3.50pm.

Talks comprise 45 minutes of speaking time plus five minutes for questions and discussion.

#### Information for speakers

Researchers in all pure mathematics fields attend our seminars, so please aim your presentation at a general mathematical audience.

#### Contact us

To volunteer to talk or to suggest a speaker, email Ole Warnaar or Travis Scrimshaw.