Let W be a classical Weyl group and ∏ be the corresponding system of simple roots. For w∈ W, let R(w)={α∈∏|l(ws_α)【l(w)}, where we denote by s_α the simple reflection in the hyperplane orthogonal to α for α...Let W be a classical Weyl group and ∏ be the corresponding system of simple roots. For w∈ W, let R(w)={α∈∏|l(ws_α)【l(w)}, where we denote by s_α the simple reflection in the hyperplane orthogonal to α for α∈∏ and by l(w)the minimal length of an expression of w as a product of simple reflections. To any Weyl group one can associate a展开更多
In 2014, Vargas first defined a super-shuffle product and a cut-box coproduct on permutations. In 2020, Aval, Bergeron and Machacek introduced the super-shuffle product and the cut-box coproduct on labeled simple grap...In 2014, Vargas first defined a super-shuffle product and a cut-box coproduct on permutations. In 2020, Aval, Bergeron and Machacek introduced the super-shuffle product and the cut-box coproduct on labeled simple graphs. In this paper, we generalize the super-shuffle product and the cut-box coproduct from labeled simple graphs to (0,1)-matrices. Then we prove that the vector space spanned by (0,1)-matrices with the super-shuffle product is a graded algebra and with the cut-box coproduct is a graded coalgebra.展开更多
基金supported by National Natural Science Foundation of China(Grant No. 10731070)the Doctoral Program of Higher Educationthe Fundamental Research Funds for the Central University
文摘In the present paper we determine the representation type of the 0-Hecke algebra of a finite Coxeter group.
基金Project supported by the National Natural Science Foundation of China.
文摘Let W be a classical Weyl group and ∏ be the corresponding system of simple roots. For w∈ W, let R(w)={α∈∏|l(ws_α)【l(w)}, where we denote by s_α the simple reflection in the hyperplane orthogonal to α for α∈∏ and by l(w)the minimal length of an expression of w as a product of simple reflections. To any Weyl group one can associate a
文摘In 2014, Vargas first defined a super-shuffle product and a cut-box coproduct on permutations. In 2020, Aval, Bergeron and Machacek introduced the super-shuffle product and the cut-box coproduct on labeled simple graphs. In this paper, we generalize the super-shuffle product and the cut-box coproduct from labeled simple graphs to (0,1)-matrices. Then we prove that the vector space spanned by (0,1)-matrices with the super-shuffle product is a graded algebra and with the cut-box coproduct is a graded coalgebra.
