  In \cite{JS} Jensen and Su constructed 0-Schur algebras on double flag
varieties. The construction leads to a presentation of 0-Schur algebras using
quivers with relations and the quiver approach naturally gives rise to a new
class of algebras. That is, the path algebras defined on the quivers of 0-Schur
algebras with relations modified from the defining relations of 0-Schur
algebras by a tuple of parameters $\ut$. In particular, when all the entries of
$\ut$ are 1, we have 0-Schur algerbas. When all the entries of $\ut$ are zero,
we obtain a class of degenerate 0-Schur algebras. We prove that the degenerate
algebras are associated graded algebras and quotients of 0-Schur algebras.
Moreover, we give a geometric interpretation of the degenerate algebras using
double flag varieties, in the same spirit as \cite{JS}, and show how the
centralizer algebras are related to nil-Hecke algebras and nil-Temperly-Lieb
algebras
