On the affine Springer fibers inside the invariant center of the small quantum group
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866914613417738240 |
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| author | Hemelsoet, Nicolas Kivinen, Oscar Lachowska, Anna |
| author_facet | Hemelsoet, Nicolas Kivinen, Oscar Lachowska, Anna |
| contents | Let $\mathfrak{u}_ζ^\vee$ denote the small quantum group associated with a simple Lie algebra $\mathfrak{g}^\vee$ and a root of unity $ζ$. In [9], a geometric realization of $Z(\mathfrak{u}_ζ^\vee)^{G^\vee}$, the $G^\vee$-invariant part of the center of $\mathfrak{u}_ζ^\vee$, was proposed. We compute the dimension of the geometric subalgebra of the center and in the case where $G=SL_n$, we study a bigraded refinement of the result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_09700 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the affine Springer fibers inside the invariant center of the small quantum group Hemelsoet, Nicolas Kivinen, Oscar Lachowska, Anna Representation Theory Algebraic Geometry Quantum Algebra Let $\mathfrak{u}_ζ^\vee$ denote the small quantum group associated with a simple Lie algebra $\mathfrak{g}^\vee$ and a root of unity $ζ$. In [9], a geometric realization of $Z(\mathfrak{u}_ζ^\vee)^{G^\vee}$, the $G^\vee$-invariant part of the center of $\mathfrak{u}_ζ^\vee$, was proposed. We compute the dimension of the geometric subalgebra of the center and in the case where $G=SL_n$, we study a bigraded refinement of the result. |
| title | On the affine Springer fibers inside the invariant center of the small quantum group |
| topic | Representation Theory Algebraic Geometry Quantum Algebra |
| url | https://arxiv.org/abs/2205.09700 |