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In \cite{JS} Jensen and Su constructed 0-Schur algebras on double flagvarieties. The construction leads to a presentation of 0-Schur algebras usingquivers with relations and the quiver approach naturally gives rise to a newclass of algebras. That is, the path algebras defined on the quivers of 0-Schuralgebras with relations modified from the defining relations of 0-Schuralgebras 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 degeneratealgebras are associated graded algebras and quotients of 0-Schur algebras.Moreover, we give a geometric interpretation of the degenerate algebras usingdouble flag varieties, in the same spirit as \cite{JS}, and show how thecentralizer algebras are related to nil-Hecke algebras and nil-Temperly-Liebalgebras

Degenerate 0-Schur algebras and Nil-Temperley-Lieb algebras