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2024年10月31日(木) 15:30~17:00
大阪公立大学 杉本キャンパス 理学部E棟4階 E408 大講義室 (およびZoomのハイブリッド形式の予定)
村田 遼人氏(東京大学)
Affine highest weight structures on module categories over quiver Hecke algebras
Associated with a symmetrizable Kac-Moody algebra $\mathfrak{g}$, the module category over the quiver Hecke algebra provide a categorification of the quantum group $U_q(\mathfrak{n}^-)$. For any Weyl group element $w$, there is a full subcategory $\mathscr{C}_w^{\text{f.g.}}$ corresponding to the quantum unipotent subgroup $U_q(\mathfrak{n}^- \cap w \mathfrak{n}^+)$, which is important from the perspective of monoidal categorification of cluster algebras. In this talk, we show that $\mathscr{C}_w^{\text{f.g.}}$ is an affine highest weight category by concretely realizing the standard modules using determinantial modules. If time permits, we will explain how this result can be applied to categorify PBW bases for arbitrary quantum affine algebras.