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• W2950572926 startingPage "61" @default.
• W2950572926 abstract "Suppose that $M$ is an even lattice with dual $M^{*}$ and level $N$. Then the group $Mp_{2}(mathbb{Z})$, which is the unique non-trivial double cover of $SL_{2}(mathbb{Z})$, admits a representation $rho_{M}$, called the Weil representation, on the space $mathbb{C}[M^{*}/M]$. The main aim of this paper is to show how the formulae for the $rho_{M}$-action of a general element of $Mp_{2}(mathbb{Z})$ can be obtained by a direct evaluation which does not depend on ``external objects'' such as theta functions. We decompose the Weil representation $rho_{M}$ into $p$-parts, in which each $p$-part can be seen as subspace of the Schwartz functions on the $p$-adic vector space $M_{mathbb{Q}_{p}}$. Then we consider the Weil representation of $Mp_{2}(mathbb{Q}_{p})$ on the space of Schwartz functions on $M_{mathbb{Q}_{p}}$, and see that restricting to $Mp_{2}(mathbb{Z})$ just gives the $p$-part of $rho_{M}$ again. The operators attained by the Weil representation are not always those appearing in the formulae from 1964, but are rather their multiples by certain roots of unity. For this, one has to find which pair of elements, lying over a matrix in $SL_{2}(mathbb{Q}_{p})$, belong to the metaplectic double cover. Some other properties are also investigated." @default.
• W2950572926 created "2019-06-27" @default.
• W2950572926 creator A5051460856 @default.
• W2950572926 date "2015-06-01" @default.
• W2950572926 modified "2023-10-03" @default.
• W2950572926 title "A p-adic approach to the Weil representation of discriminant forms arising from even lattices" @default.
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• W2950572926 doi "https://doi.org/10.1007/s40316-015-0034-6" @default.
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