1. Deformed Cartan matrices and generalized preprojective algebras II: General type
- Author
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Fujita, Ryo and Murakami, Kota
- Subjects
Mathematics - Representation Theory ,Mathematics - Quantum Algebra ,16G20, 17B37, 16W50, 17B67, 81R50 - 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 Gei\ss-Leclerc-Schr\"oer. 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., Comment: 27 pages, v2: final version, minor corrections
- Published
- 2023
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