Explore the intricacies of component tableaux in this 58-minute lecture by Anthony Joseph, presented at the International Centre for Theoretical Sciences. Delve into the algebraic and combinatorial methods in representation theory as part of a comprehensive program featuring workshops, mini-courses, and lectures by renowned experts. Gain insights into vertex algebras, quantum affine algebras, quantum superalgebras, and reductive groups. Discover how this field connects to other areas of mathematics and physics while celebrating the contributions of Vyjayanthi Chari. Suitable for graduate students, postdoctoral scholars, and researchers interested in Lie theory and related representation theory.