We study the tight representation of a semilattice in by some examples. Then we introduce the concept of the complex tight representation of an inverse semigroup by the concept of the tight representation of the semilattice of idempotents of in . Specifically we describe the tight representation of a 0--unitary inverse semigroup and prove that if is a tight semilattice representation of the 0--unitary inverse semigroup in , then is a complex tight representation.
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