arXiv subjects
Publications and source records attributed to Manish Mishra.
Let $G$ be a connected reductive group defined over a non archimedean local field $k$. A theorem of Bernstein states that for any compact open subgroup $K$ of $G(k)$, there are, up to unramified twists, only finitely many $K$-spherical supercuspidal representations of $G(k)$. We prove an analogous result on the Galois side of the Langlands correspondence.
We describe the image, under the local Langlands correspondence for tori, of the characters of a torus which are trivial on its Iwahori subgroup. Let $k$ be a non-archimedian local field. Let $\boldsymbol{G}$ be a connected reductive group defined over $k$, which is quasi-split and split over a tamely ramified extension. Let $K$ be a special maximal parahoric subgroup of $\boldsymbol{G}(k)$. To the class of representations of $\boldsymbol{G}(k)$, having a non-zero vector fixed under $K$, we establish a bijection, in a natural way, with the twisted semi-simple conjugacy classes of the inertia fixed subgroup of the dual group $\hat{\boldsymbol{G}}$. These results generalize the well known classical results to the ramified case.
Let $\boldsymbol{G}$ be an unramified connected reductive group defined over a non-archemedian local field $k$ and let $\boldsymbol{T}$ be a maximal torus in $\boldsymbol{G}.$ Let $λ$ be an unramified character of $\boldsymbol{T}.$ Then the conjugacy classes of hyperspecial subgroups of $\boldsymbol{G}(k)$ is a principal homogenous space for a certain finite abelian group $\hatΩ$. Also, the $L$-packet $Π(φ_λ)$ associated to $λ$ is parametrized by an abelian group $\hat{R}$. We show that $\hat{R}$ is naturally a homogenous space for $\hatΩ$. Further, let $π_ρ\inΠ(φ_λ)$, where $ρ\in\hat{R}$ and let $[K]$ denote the conjugacy class of hyperspecial subgroup $K.$ Then we show that $π_ρ^{K}\neq0$ if and only if $π_{ω\cdotρ}^{K_ω}\neq0$ where $ω\in\hatΩ$ and $K_ω$ is any hyperspecial subgroup in the conjugacy class $ω\cdot[K]$.
OLAP systems operate on historical data and provide answers to analysts queries. Recent in-memory implementations provide significant performance improvement for real time ad-hoc analysis. Philosophy and techniques of what-if analysis on data warehouse and in-memory data store based OLAP systems have been covered in great detail before but exploration of new dimension value (attribute) introduction has been limited in the context of what-if analysis. We extend the approach of Andrey Balmin et al of using select modify operator on data graph to introduce new values for dimensions and measures in a read-only in-memory data store as scenarios. Our system constructs scenarios without materializing the rows and stores the row information as queries. The rows associated with the scenarios are constructed as and when required by an ad-hoc query.