A field-independent filtration of Δ^{(n,m)} Sym^d E with layers Sym^{n+m} Sym^{d-k} E ⊗ Δ^{(n-k,m-k)} Sym^k E categorifies the Cartan product rule of U_q(sl_2).
Tres lecciones en combinatoria algebraica. II. Las funciones sim\'etricas y la teor\'{\i}a de representaciones
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abstract
En esta serie de tres articulos, damos una exposicion de varios resultados y problemas abiertos en tres areas de la combinatoria algebraica y geometrica: las matrices totalmente no negativas, las representaciones del grupo simetrico, y los arreglos de hiperplanos. Esta segunda parte trata la coneccion entre las funciones simetricas y la teoria de representaciones. In this series of three articles, we give an exposition of various results and open problems in three areas of algebraic and geometric combinatorics: totally non-negative matrices, representations of the symmetric group, and hyperplane arrangements. This second part treats the connection between symmetric functions and representation theory.
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A field-independent filtration of plethystic modules for $\mathrm{SL}_2(\mathbb{F})$ that categorifies a product rule for the Cartan subalgebra of $\mathcal{U}_q(\mathfrak{sl}_2)$
A field-independent filtration of Δ^{(n,m)} Sym^d E with layers Sym^{n+m} Sym^{d-k} E ⊗ Δ^{(n-k,m-k)} Sym^k E categorifies the Cartan product rule of U_q(sl_2).