A generalization of quantum Lakshmibai-Seshadri paths for arbitrary weights
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929267735003136 |
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| author | Kouno, Takafumi Naito, Satoshi |
| author_facet | Kouno, Takafumi Naito, Satoshi |
| contents | We construct an injective weight-preserving map (called the forgetful map) from the set of all admissible subsets in the quantum alcove model associated to an arbitrary weight. The image of this forgetful map can be explicitly described by introducing the notion of "interpolated quantum Lakshmibai-Seshadri (QLS for short) paths", which can be thought of as a generalization of quantum Lakshmibai-Seshadri paths. As an application, we reformulate, in terms of interpolated QLS paths, an identity of Chevalley type for the graded characters of Demazure submodules of a level-zero extremal weight module over a quantum affine algebra, which is a representation-theoretic analog of the Chevalley formula for the torus-equivariant $K$-group of a semi-infinite flag manifold. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_04560 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A generalization of quantum Lakshmibai-Seshadri paths for arbitrary weights Kouno, Takafumi Naito, Satoshi Combinatorics Representation Theory Primary 05E10, Secondary 14N15, 14M15 We construct an injective weight-preserving map (called the forgetful map) from the set of all admissible subsets in the quantum alcove model associated to an arbitrary weight. The image of this forgetful map can be explicitly described by introducing the notion of "interpolated quantum Lakshmibai-Seshadri (QLS for short) paths", which can be thought of as a generalization of quantum Lakshmibai-Seshadri paths. As an application, we reformulate, in terms of interpolated QLS paths, an identity of Chevalley type for the graded characters of Demazure submodules of a level-zero extremal weight module over a quantum affine algebra, which is a representation-theoretic analog of the Chevalley formula for the torus-equivariant $K$-group of a semi-infinite flag manifold. |
| title | A generalization of quantum Lakshmibai-Seshadri paths for arbitrary weights |
| topic | Combinatorics Representation Theory Primary 05E10, Secondary 14N15, 14M15 |
| url | https://arxiv.org/abs/2403.04560 |