Skew Howe duality and limit shapes of Young diagrams
Journal of the London Mathematical Society, Volume 109, Issue 1, January 2024.Abstract We consider the skew Howe duality for the action of certain dual pairs of Lie groups (G1,G2)$(G_1, G_2)$ on the exterior algebra ⋀(Cn⊗Ck)$\bigwedge (\mathbb {C}^{n} \otimes \mathbb {C}^{k})$ as a probability measure on Young diagrams by the decomposition into the sum of irreducible representations. We prove a combinatorial version of this skew
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