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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.10157 |
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Table of Contents:
- For the quiver Hecke algebra $R$, let $R\hbox{-gmod}$ be the category of finite-dimensional graded $R$-modules, and let $\widetilde{R\hbox{-gmod}[w]}$ be the localization of $R\hbox{-gmod}$. Kashiwara and the second author showed the set of equivalence classes of simple objects up to grading shifts $\mathrm{Irr}(\widetilde{R\hbox{-gmod}[w]})$ in $\widetilde{R\hbox{-gmod}[w]}$ has a crystal structure, and $\mathrm{Irr}(\widetilde{R\hbox{-gmod}[w]})$ is isomorphic to the so-called cellular crystal $\mathbb B_{\mathbf i}$. This isomorphism induces a function $\varepsilon_i^*$ on $\mathbb B_{\mathbf i}$. We give an explicit formula of $\varepsilon_i^*$, and using this formula, we give a characterization of the unit object of $\widetilde{R\hbox{-gmod}[w]}$ for the case of classical finite types.