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Cartan matrix over the 0-Hecke algebra of type F4

陈承东Chen Cheng-Dong Qian Jin

C. Cheng-Dong, Q. Jin. Journal of Algebra 252 (2002) 84-94,-0001,():

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摘要/描述

Let (W, S) be the finite Weyl group with S as its Coxeter generating set. For w ∈W, let R(w) = {si ∈ S | l(wsi) < l(w)} and L(w) = {si ∈ S | l(siw) < l(w)}, where we denote 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 corresponding finite-dimensional algebra called 0-Hecke algebra H where K is any field. Norton [J. Austral. Math. Soc. Ser. A 27 (1979)337–357] pointed out that the principal indecomposable modules and the irreduciblemodules over the 0-Hecke algebra H parametrized by a subset J of S. We denote by U(Jˆ) and M(Jˆ) respectively the principal indecomposable module and the irreducible module parametrized by J . For two subset J , L of S, let CJL = the number of times M(L) is a composition factor of U(Jˆ). Norton [J. Austral. Math. Soc. Ser. A 27 (1979)337–357] shown that CJL = |YL ∩ (YJ )−1| where YL = {w ∈W|R(w) = L} and(YJ)−1 = {w ∈W | L(w) = J}. In this article, we describe explicitly CJL for the 0-Hecke algebra of type F4 by applying the canonical expression of every element in theWeyl group of type F4. Thus we determine the Cartan matrix over the 0-Hecke algebra of type F4.

版权说明:以下全部内容由陈承东上传于   2007年03月02日 14时00分44秒,版权归本人所有。

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