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SYNTAX: process which plays a crucial role in the definition of a blocking category and thus in that of a barrier. Roughly, a category is L-marked iff it is theta-marked by a lexical head. EXAMPLE: in (i)

(i)  John fixed the car in a stupid way
the verb fix L-marks its direct object NP the car, but not the subject John (because this is assumed to receive its theta-role not from V0 directly, but from VP, which is not a lexical head), nor the adjunct in a stupid way (which is not theta-marked at all). (Absence of) L-marking is invoked to explain the Subject Condition and the Adjunct Condition. EXAMPLE: : only in (ii)a is who moved out of an L-marked phrase (=/= barrier), hence the contrast between (ii)a and b.
(ii) a    who did you see [ a picture of t]?
     b  * who did [a picture of t] upset you?
Chomsky's (1986b) definition of L-marking is (iii).
(iii) Where alpha is a lexical category, alpha L-marks beta iff beta 
      agrees with the head of gamma that is theta-governed by alpha
This definition entails that it is not only the theta-marked category itself which can be L-marked, but also its head (which of course agrees with itself) and its specifier if this agrees with the head under specifier-head agreement.
LIT. Chomsky, N. (1986b)