Skew Howe Duality and Limit Shapes for Young Diagrams

Explore a mathematical lecture examining the relationship between skew Howe duality and limit shapes for Young diagrams, delivered by Olga Postnova from the Euler International Mathematical Institute. Delve into the exterior algebra of tensor products of complex vector spaces and their decomposition into bimodules through the lens of GL(n) x GL(k) dual pairs. Learn how lattice paths on lozenge tilings of partial hexagonal domains provide a combinatorial interpretation of skew Howe duality, leading to product formulas for q-deformations of multiplicities. Examine probability measures on Young diagrams and discover the uniform convergence to limit shapes as dimensions approach infinity. Based on collaborative research with Anton Nazarov and Travis Scrimshaw, the presentation offers a deep exploration of these mathematical concepts within the framework of the BIMSA-Tsinghua Quantum Symmetry Seminar series.