Matthiessen (1995: 715):
The verbal group is a group of verbs - one lexical verb and one or more auxiliaries. It is organised both univariately and multivariately. The principles will be discussed below; the univariate structure is a simple hypotactic one, realised progressively — α –> β –> γ –> δ (as in α must β have γ been going δ to leave) and so on.
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[1] This is misleading. The elements of the univariate structure of the verbal group are not words. Halliday & Matthiessen (2014: 398-9):
… the elements of the logical structure are not the individual words but certain rather more complex elements. … The logical structure of the verbal group realises the system of tense. … The primary tense is that functioning as Head, shown as α. This is the Deictic tense: past, present or future relative to the speech event. The modifying elements, at β and beyond, are secondary tenses; they express past, present or future relative to the time selected in the previous tense. Realisations are shown in Table 6-12.
And so, importantly, the Event does not figure as an element in the univariate structure. Halliday (1985: 184n):
A major point of difference between the verbal group and the nominal group is that the Event (unlike the Thing) is not the point of departure for the recursive modifying relationship. Hence it does not figure as an element in the notation.
[2] To be clear, this misrepresents the univariate structure of the verbal group. Only three features, not four, are selected in this verbal group: modal, past and future, realised as:
[must] [have + V-en] [be going to + V]
must have been going to leave
α modal β past γ future