Combinatorial Models for Weyl Characters

We will present a simple set of axioms for combinatorial objects that provide models for "Weyl characters"--the characters of representations of semisimple Lie groups/algebras, or more generally for "Kac-Weyl" characters--the analogues for Kac-Moody algebras. Given any set of objects fitting the axioms, it is trivial to derive rules for computing weight multiplicity, tensor product multiplicity, and branching (restriction) rules.

Examples include the familiar semistandard tableaux and Littlewood Richardson rule in type A, and the (probably less familiar) Lakshmibai Seshadri chains for all types.

No knowledge of representation theory will be needed or assumed for the talk, although familiarity with Weyl groups will be useful.