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- W4366564148 abstract "Let $G$ be a compact group with two given subgroups $H$ and $K$. Let $pi$ be an irreducible representation of $G$ such that its space of $H$-invariant vectors as well as the space of $K$-invariant vectors are both one dimensional. Let $v_H$ (resp. $v_K$) denote an $H$-invariant (resp. $K$-invariant) vector of unit norm in a given $G$-invariant inner product $langle ~,~ rangle_pi$ on $pi$. We are interested in calculating the correlation coefficient [c(pi;H,K) = |langle v_H,v_K rangle_pi|^2.] In this paper, we compute the correlation coefficient of an irreducible representation of the multiplicative group of the $p$-adic quaternion algebra with respect to any two tori. In particular, if $pi$ is such an irreducible representation of odd minimal conductor with non-trivial invariant vectors for two tori $H$ and $K$, then its root number $varepsilon(pi)$ is $pm 1$ and $c(pi; H, K)$ is non-vanishing precisely when $varepsilon(pi) = 1$." @default.
- W4366564148 created "2023-04-22" @default.
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- W4366564148 date "2023-04-19" @default.
- W4366564148 modified "2023-10-01" @default.
- W4366564148 title "Toric periods for a $p$-adic quaternion algebra" @default.
- W4366564148 doi "https://doi.org/10.48550/arxiv.2304.09765" @default.
- W4366564148 hasPublicationYear "2023" @default.
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