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- W2883004536 abstract "Let $mathfrak{o}$ be the ring of integers of a non-Archimedean local field $F$ with finite residue field of even characteristic and maximal ideal $mathfrak{p}.$ Let $mathrm{e}(mathfrak{o})$ denotes the ramification index of $mathfrak{o}$ in case $mathfrak{o}$ has characteristic zero. We prove that the abscissa of convergence of representation zeta function of Special Linear group $mathrm{SL}_2(mathfrak{o})$ is $1.$ We prove that for any $mathfrak{o}$ of characteristic zero with the residue field of cardinality $q$ such that $2 mid q$ the group algebras $mathbb C[mathrm{SL}_2( mathfrak{o}/mathfrak{p}^{2 r})]$ and $mathbb C[mathrm{SL}_2(mathbb F_q[t]/(t^{2r}))]$ are not isomorphic for any $r > mathrm{e}(mathfrak{o}).$ Further we give a construction of all primitive irreducible representations of groups $mathrm{SL}_2left (mathbb F_q[t]/(t^{2r}) right) $ for all $r geq 1$ and of groups $mathrm{SL}_2( mathfrak{o}/mathfrak{p}^{2 r}),$ where $mathfrak{o}$ has characteristic zero and $r geq 2mathrm{e}(mathfrak{o}).$" @default.
- W2883004536 created "2018-08-03" @default.
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- W2883004536 date "2018-07-17" @default.
- W2883004536 modified "2023-09-27" @default.
- W2883004536 title "Representation Growth of Special Compact Linear Groups of Order Two" @default.
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