Speaker:  Goran Omerdic, Western Kentucky University

Title:  Distributive lattice models for one-rowed representations of the classical Lie algebras

Abstract:

Lie algebras are canonically used to describe the symmetries of continuous functions. Such algebras are rich in enumerative properties. We consider the classical Lie algebras, which are comprised of the "special linear," "symplectic" and "orthogonal" Lie algebras through a lens of algebraic combinatorics, using colored modular and distributive lattice models to describe said properties. Research related to special linear, symplectic and odd orthogonal Lie algebras has been fruitful, yielding families of lattice models and related coefficients to generate direct graphs. We use these methods to explore the properties of even orthogonal Lie algebras, their lattice and one-rowed tableau representations.