arXiv subjects
Publications and source records attributed to Cemile Kurkoglu.
An elliptic exceptional Belyi covering is a connected Belyi covering uniquely determined by its ramification scheme or the respective dessin d'enfant when the underlying compact Riemann surface has genus 1. We give our Maple algorithm and table that display our calculations for elliptic exceptional Belyi coverings up to degree 12.
Exceptional Belyi covering is a connected Belyi covering uniquely determined by its ramification scheme or the respective dessin d'enfant. We focus on rational exceptional Belyi coverings of compact Riemann surfaces of genus 0. Well known examples are cyclic, dihedral, and Chebyshev coverings. Using Maple, we identified all rational exceptional Belyi coverings up to degree 15. Their Belyi functions were calculated for degrees up to 6 along with some for degree 7. We also found new infinite series.
Let $\bf{G}$ be a split connected reductive group over a finite extension $F$ of $\mathbb Q_p$, and let $\bf{T} \subset \bf{B} \subset \bf{G}$ be a maximal split torus and a Borel subgroup, respectively. Denote by $G = {\bf{G}}(F)$ and $B= {\bf{B}}(F)$ their groups of $F$-valued points and by $\mathfrak g = \rm Lie(G)$ and $\mathfrak b = \rm Lie(B)$ their Lie algebras. Let $\mathcal O^\infty$ be the thick category $\mathcal O$ for $(\mathfrak g,\mathfrak b)$, and denote by $\mathcal{O}^\infty_{\rm alg} \subset \mathcal{O}^\infty$ the full subcategory consisting of objects whose weights are in $X^*(\bf{T})$. Both are Serre subcategories of the category of all $U$-modules, where $U = U(\mathfrak g)$. We show first that the functor $\mathbb D^\mathfrak g = \rm RHom_U(-,U)$ preserves $D^b(U)_{\mathcal{O}^\infty_{\rm alg}}$, and we deduce from a result of Coulembier-Mazorchuk that the latter category is equivalent to $D^b(\mathcal O^\infty_{\rm alg})$.