Vyjayanthi Chari
University of California
December 12, 2024
Quantum affine algebras, affine Hecke algebras and the BGG Category O.: We give an overview of the connection between the representation theory of the quantum affine algebra associated to $sl_n$ and the complex smooth representations of $GL_N(F)$ where $F$ is a non-archimedean field. This connection goes through the affine/ degenerate Hecke algebra, which is also related to the $BGG$ category of the reductive complex Lie algebra $gl_r$. We discuss some recent results with Matheus Brito on the quantum side which allows us to compute certain KL--coefficients in the category $\mathcal{O}$.
University of California
December 12, 2024
Quantum affine algebras, affine Hecke algebras and the BGG Category O.: We give an overview of the connection between the representation theory of the quantum affine algebra associated to $sl_n$ and the complex smooth representations of $GL_N(F)$ where $F$ is a non-archimedean field. This connection goes through the affine/ degenerate Hecke algebra, which is also related to the $BGG$ category of the reductive complex Lie algebra $gl_r$. We discuss some recent results with Matheus Brito on the quantum side which allows us to compute certain KL--coefficients in the category $\mathcal{O}$.