Let $F$ be a non-Archimedean locally compact field‎. ‎Let $sigma$ and $tau$ be finite-dimensional representations of the Weil-Deligne group of $F$‎. ‎We give strong upper and lower bounds for the Artin and Swan exponents of $sigmaotimestau$ in terms of those of $sigma$ and $tau$‎. ‎We give a different lower bound in terms of $sigmaotimeschecksigma$ and $tauotimeschecktau$‎. ‎Using the Langlands...

The specificity of DNA-dependent RNA polymerase for target promotes is largely due to the replaceable sigma subunit that it carries. Multiple sigma proteins, each conferring a unique promoter preference on RNA polymerase, are likely to be present in all bacteria; however, their abundance and diversity have been best characterized in Bacillus subtilis, the bacterium in which multiple sigma facto...