第7回

日時

2025年3月28日(金) 15:30~17:00

場所

i-Siteなんば S1 (およびZoomのハイブリッド形式の予定)

講演者

藤田 遼氏(京都大学数理解析研究所)

タイトル

Singularities of R-matrices and E-invariants for Dynkin quivers

アブストラクト

In the theory of finite-dimensional representations of affine quantum groups, the singularities of (normalized) R-matrices play an important role as they encode the non-commutativity of tensor product representations. However, computing the pole order of R-matrices is difficult in general, and so far explicitly known only for fundamental and Kirillov—Reshetikhin modules. In this talk, we restrict our attention to a certain subcategory of representations which monoidally categorifies a cluster algebra of finite type (known as Hernandez—Leclerc’s level-one subcategory), and show that the pole order of R-matrices is computable for any irreducible representations as the dimension of E-invariants (analog of extension groups) of decorated representations of Dynkin quivers. This manifests a correspondence of numerical characteristics between monoidal and additive categorifications of cluster algebras of finite type. Our proof is inspired by the previous studies of perverse sheaves on quiver varieties due to Nakajima and Kimura—Qin.

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