Markov traces on degenerate cyclotomic Hecke algebras
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908663842603008 |
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| author | Zhao, Deke |
| author_facet | Zhao, Deke |
| contents | Let $H_n(\boldsymbol{u})$ be the degenerate cyclotomic Hecke algebra with parameter $\boldsymbol{u}=(u_1, \ldots, u_m)$ over $\mathbb{C}(\boldsymbol{u})$. We define and construct the (non-)normalized Markov traces on the sequence $\{H_n(\boldsymbol{u})\}_{n=1}^{\infty}$. This allows us to provide a canonical symmetrizing form on $H_n(\boldsymbol{u})$ and show that the Brudan--Kleshchev trace on $H_n(\boldsymbol{u})$ is a specialization of the non-normalized Markov traces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09372 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Markov traces on degenerate cyclotomic Hecke algebras Zhao, Deke Representation Theory Rings and Algebras Let $H_n(\boldsymbol{u})$ be the degenerate cyclotomic Hecke algebra with parameter $\boldsymbol{u}=(u_1, \ldots, u_m)$ over $\mathbb{C}(\boldsymbol{u})$. We define and construct the (non-)normalized Markov traces on the sequence $\{H_n(\boldsymbol{u})\}_{n=1}^{\infty}$. This allows us to provide a canonical symmetrizing form on $H_n(\boldsymbol{u})$ and show that the Brudan--Kleshchev trace on $H_n(\boldsymbol{u})$ is a specialization of the non-normalized Markov traces. |
| title | Markov traces on degenerate cyclotomic Hecke algebras |
| topic | Representation Theory Rings and Algebras |
| url | https://arxiv.org/abs/2409.09372 |