  This article introduces the duplex Hecke algebra, which is an infinite
dimensional algebra generated by two Hecke algebras. This concept originates
from the degenerate duplex Hecke algebra in the theory of Schur-Weyl duality
related to enhanced reductive algebraic groups. We will study the finite
dimensional natural representation of the duplex Hecke algebra on tensor space
and prove that the duplex Hecke algebra forms a duality with the Levi type
quantum group.
