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Deformed Cartan Matrices and Generalized Preprojective Algebras I: Finite Type

Fujita, Ryo Murakami, Kota 京都大学 DOI:10.1093/imrn/rnac054

2023.04

概要

We give an interpretation of the $(q, t)$-deformed Cartan matrices of finite type and their inverses in terms of bigraded modules over the generalized preprojective algebras of Langlands dual type in the sense of Geiß–Leclerc–Schröer [33]. As an application, we compute the first extension groups between the generic kernels introduced by Hernandez–Leclerc [40] and propose a conjecture that their dimensions coincide with the pole orders of the normalized $R$-matrices between the corresponding Kirillov–Reshetikhin modules.

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(R. Fujita) Research Institute for Mathematical Sciences, Kyoto University, Oiwake´matiques de JussieuKitashirakawa, Sakyo, Kyoto, 606-8502, Japan & Institut de Mathe

´ de Paris, F-75013, Paris, France

Paris Rive Gauche, Universite

Email address: rfujita@kurims.kyoto-u.ac.jp

(K. Murakami) Department of Mathematics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto, 606-8502, Japan

Email address: k-murakami@math.kyoto-u.ac.jp

...

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