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arXiv · 1705.06084

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

Bernt Tore Jensen·Xiuping Su·Guiyu Yang
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Abstract

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

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BibTeXRIS

Bernt Tore Jensen, Xiuping Su, Guiyu Yang. 2017-05-18. Degenerate 0-Schur algebras and Nil-Temperley-Lieb algebras. https://arxiv.org/abs/1705.06084

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