The tensor product of m-partition algebras as a centralizer algebra of
In this paper, we concentrate on the generalized Jones result in Kennedy and Jaish (2021) which says that [Formula: see text], the tensor product of m-partition algebras is a centralizer algebra of the action of the direct product of symmetric groups, [Formula: see text], on the k-folder tensor prod...
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| Format: | Article |
| Language: | English |
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World Scientific Publishing
2025-01-01
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| Series: | Mathematics Open |
| Subjects: | |
| Online Access: | https://www.worldscientific.com/doi/10.1142/S2811007225300010 |
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| Summary: | In this paper, we concentrate on the generalized Jones result in Kennedy and Jaish (2021) which says that [Formula: see text], the tensor product of m-partition algebras is a centralizer algebra of the action of the direct product of symmetric groups, [Formula: see text], on the k-folder tensor products [Formula: see text], where [Formula: see text]. In particular, we restrict the action of the direct products of symmetric groups, [Formula: see text], to the action of the direct product of alternating groups, [Formula: see text]. Herein, we determine the basis for the centralizer algebra and exhibit that when the centralizer is isomorphic to the tensor product of m-partition algebras, [Formula: see text]. |
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| ISSN: | 2811-0072 |