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Heads of administration in shtook, the french split down the middle (5)

Ross

I believe the answer is:

aisle

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'split down the middle' is the definition.
I can't tell whether this definition defines the answer.

'heads of administration in shtook the french' is the wordplay.
'heads of' indicates taking the first letters.
'the french' becomes 'le' ('the' in French).
The first letters of 'administration in shtook' is 'ais'.
'ais'+'le'='AISLE'

Can you help me to learn more?

(Other definitions for aisle that I've seen before include "channel" , "Passageway between pews" , "Passages between seating areas" , "way to the altar?" , "The way to get married in church?" .)

I've seen this clue in The Times.
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