On the affine Springer fibers inside the invariant center of the small quantum group
| Autor: | Hemelsoet, Nicolas, Kivinen, Oscar, Lachowska, Anna |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $\mathfrak{u}_\zeta^\vee$ denote the small quantum group associated with a simple Lie algebra $\mathfrak{g}^\vee$ and a root of unity $\zeta$. Based on the geometric realization of the center of $\mathfrak{u}_\zeta^\vee$ in [8], we use a combinatorial method to derive a formula for the dimension of a subalgebra in the $G^\vee$-invariant part of the center $Z(\mathfrak{u}_\zeta^\vee)^{G^\vee}$ of $\mathfrak{u}_\zeta^\vee$, that conjecturally coincides with the whole $G^\vee$-invariant center. In case $G=SL_n$ we study a refinement of the obtained dimension formula provided by two geometrically defined gradings. Comment: 26 pages |
| Databáze: | arXiv |
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