\label{rw:sec:notation} The table lists notation used in more than one section, with the place where it is introduced. \begingroup \small \renewcommand{\arraystretch}{1.13} \begin{longtable}{@{}>{\raggedright\arraybackslash}p{.24\textwidth} >{\raggedright\arraybackslash}p{.72\textwidth}@{}} \toprule Notation & Meaning and location \\ \midrule \endfirsthead \toprule Notation & Meaning and location \\ \midrule \endhead \bottomrule \endfoot \(X,F,\Gamma_F\) & The original curve, its function field and its absolute Galois group.\\ \(p,q,\ell,k\) & The geometric characteristic, size of the constant field, coefficient prime, and \(k=\overline{\mathbb Q}_\ell\).\\ \(\deg_F,d_v\) & Arithmetic Galois degree and the degree of a closed point \(v\); geometric Frobenius at \(v\) has degree \(-d_v\).\\ \(G,\widehat G,M,\widehat M\) & The split group, its dual, a Levi subgroup and the corresponding dual Levi.\\ \(\sigma,\nu_\sigma\) & The prescribed parameter and its character on excursion data, defined by \eqref{fl:eq:main-full-label}.\\ \(e=(I,f,\boldsymbol\gamma)\), \(S_e\), \(S_e^{\mathrm{fun}}\) & An excursion datum, its excursion operator on functions with compact support, and the transposed operator on all functions (\cite[Definitions~\xnum{I}{fl:def:weil-excursion-datum} and~\xnum{I}{fl:def:function-excursion-action}]{HuI}).\\ \(T_G,\Xi,\omega_\sigma\) & The connected centre with its reduced structure, a central lattice, and the central character of \(\sigma\) (Definition~\ref{fl:def:central-period-lattice}).\\ \(\iota\) & The fixed isomorphism \(k\simeq\mathbb C\) (Section~\ref{fl:sec:classical-descent}).\\ \(\psi,[N],\mathcal F_{N,\zeta}\) & The additive character, the quotient \(N(F)\backslash N(\mathbb A_F)\), and a Fourier coefficient (Sections~\ref{fl:sec:classical-descent} and~\ref{fl:sec:char2-d}).\\ \(\mathcal{SW}\) & The Siegel--Whittaker coefficient (Section~\ref{fl:sec:common-descent}).\\ \(x_\alpha(t),E_{a,b}\) & A root group element and an elementary matrix (Section~\ref{fl:sec:classical-descent}).\\ \(r_i(v)\) & The unipotent element attached to a vector \(v\) of the terminal space (Section~\ref{fl:sec:char2-d}).\\ \(\varrho,\varrho_i,\Pi_i\) & The standard representation \(\operatorname{Std}\sigma\) of a classical parameter, an irreducible summand of it, and the corresponding cuspidal representation of a general linear group (Section~\ref{fl:sec:classical-descent}).\\ \end{longtable} \endgroup \medskip The following terms are introduced in this paper, or are used in a sense fixed here. \begingroup \small \renewcommand{\arraystretch}{1.13} \begin{longtable}{@{}>{\raggedright\arraybackslash}p{.42\textwidth} >{\raggedright\arraybackslash}p{.54\textwidth}@{}} \toprule Term & Where it is defined \\ \midrule \endfirsthead \toprule Term & Where it is defined \\ \midrule \endhead parameter; semisimple; elliptic & Definition~\ref{fl:def:intro-parameter}\\ central lattice; invariant under \(\Xi\) & Definition~\ref{fl:def:central-period-lattice}\\ excursion summand & Definition~\ref{fl:def:full-excursion-summand}\\ automorphic realization; to realize a parameter & Section~\ref{rw:sec:III-introduction}, after \eqref{fl:eq:main-full-label}\\ descent; descent datum & Section~\ref{fl:sec:orthogonal-descent}\\ \bottomrule \end{longtable} \endgroup