On the Grothendieck ring of a quasireductive Lie superalgebra
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866908604567650304 |
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| author | Gorelik, Maria Serganova, Vera Sherman, Alexander |
| author_facet | Gorelik, Maria Serganova, Vera Sherman, Alexander |
| contents | Given a Lie superalgebra $\mathfrak{g}$ and a maximal quasitoral subalgebra $\mathfrak{h}$, we consider properties of restrictions of $\mathfrak{g}$-modules to $\mathfrak{h}$. This is a natural generalization of the study of characters in the case when $\mathfrak{h}$ is an even maximal torus. We study the case of $\mathfrak{g}=\mathfrak{q}_n$ with $\mathfrak{h}$ a Cartan subalgebra, and prove several special properties of the restriction in this case, including an explicit realization of the $\mathfrak{h}$-supercharacter ring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_07709 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the Grothendieck ring of a quasireductive Lie superalgebra Gorelik, Maria Serganova, Vera Sherman, Alexander Representation Theory Given a Lie superalgebra $\mathfrak{g}$ and a maximal quasitoral subalgebra $\mathfrak{h}$, we consider properties of restrictions of $\mathfrak{g}$-modules to $\mathfrak{h}$. This is a natural generalization of the study of characters in the case when $\mathfrak{h}$ is an even maximal torus. We study the case of $\mathfrak{g}=\mathfrak{q}_n$ with $\mathfrak{h}$ a Cartan subalgebra, and prove several special properties of the restriction in this case, including an explicit realization of the $\mathfrak{h}$-supercharacter ring. |
| title | On the Grothendieck ring of a quasireductive Lie superalgebra |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2206.07709 |