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arXiv · 2302.14315

Deformed Cartan matrices and generalized preprojective algebras II: General type

Ryo Fujita·Kota Murakami
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Abstract

We propose a definition of deformed symmetrizable generalized Cartan matrices with several deformation parameters, which admit a categorical interpretation by graded modules over the generalized preprojective algebras in the sense of Geiß-Leclerc-Schröer. Using the categorical interpretation, we deduce a combinatorial formula for the inverses of our deformed Cartan matrices in terms of braid group actions. Under a certain condition, which is satisfied in all the symmetric cases or in all the finite and affine cases, our definition coincides with that of the mass-deformed Cartan matrices introduced by Kimura-Pestun in their study of quiver $\mathcal{W}$-algebras.

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Ryo Fujita, Kota Murakami. 2024-02-04. Deformed Cartan matrices and generalized preprojective algebras II: General type. https://doi.org/10.1007/s00209-023-03386-4

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