Stabilization phenomena in Kac-Moody algebras and quiver varieties
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2005
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| _version_ | 1866917614221000704 |
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| author | Webster, Ben |
| author_facet | Webster, Ben |
| contents | Let X be the Dynkin diagram of a symmetrizable Kac-Moody algebra, and X_0 a subgraph with all vertices of degree 1 or 2. Using the crystal structure on the components of quiver varieties for X, we show that if we expand X by extending X_0, the branching multiplicities and tensor product multiplicities stabilize, provided the weights involved satisfy a condition which we call ``depth'' and are supported outside $X_0$. This extends a theorem of Kleber and Viswanath.
Furthermore, we show that the weight multiplicities of such representations are polynomial in the length of X_0, generalizing the same result for A_\ell by Benkart, et al. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0505619 |
| institution | arXiv |
| publishDate | 2005 |
| record_format | arxiv |
| spellingShingle | Stabilization phenomena in Kac-Moody algebras and quiver varieties Webster, Ben Representation Theory 17B67 Let X be the Dynkin diagram of a symmetrizable Kac-Moody algebra, and X_0 a subgraph with all vertices of degree 1 or 2. Using the crystal structure on the components of quiver varieties for X, we show that if we expand X by extending X_0, the branching multiplicities and tensor product multiplicities stabilize, provided the weights involved satisfy a condition which we call ``depth'' and are supported outside $X_0$. This extends a theorem of Kleber and Viswanath. Furthermore, we show that the weight multiplicities of such representations are polynomial in the length of X_0, generalizing the same result for A_\ell by Benkart, et al. |
| title | Stabilization phenomena in Kac-Moody algebras and quiver varieties |
| topic | Representation Theory 17B67 |
| url | https://arxiv.org/abs/math/0505619 |