Let(W,S)be the affine Weyl group of type B_(2),on which we consider the length function e from W to N and the Bruhat order≤.For y<w in W,letμ(y,w)be the coefficient of q^(1/2(e(w)-e(y)-1)) in Kazhdan-Lusztig poly...Let(W,S)be the affine Weyl group of type B_(2),on which we consider the length function e from W to N and the Bruhat order≤.For y<w in W,letμ(y,w)be the coefficient of q^(1/2(e(w)-e(y)-1)) in Kazhdan-Lusztig polynomial P_(y,w)∈Z[q].We determine someμ(y,w)for y∈c_(0) and w∈c_(2),where c0 is the lowest two-sided cell of B_(2) and c_(2) is the higher one.Furthermore,we get some consequences using left or right strings and some properties of leading coefficients.展开更多
The polynomial-like iterative equation is an important form of functional equations, in which iterates of the unknown function are linked in a linear combination. Most of known results were given for the given functio...The polynomial-like iterative equation is an important form of functional equations, in which iterates of the unknown function are linked in a linear combination. Most of known results were given for the given function to be monotone. We discuss this equation for continuous solutions in the case that the given function is a PM(piecewise monotone) function, a special class of non-monotonic functions. Using extension method, we give a general construction of solutions for the polynomial-like iterative equation.展开更多
基金Supported in part by the Natural Science Foundation of China(Grant no.11101233)Beijing Youth Top-notch Talent Support Program(Grant no.21351918007).
文摘Let(W,S)be the affine Weyl group of type B_(2),on which we consider the length function e from W to N and the Bruhat order≤.For y<w in W,letμ(y,w)be the coefficient of q^(1/2(e(w)-e(y)-1)) in Kazhdan-Lusztig polynomial P_(y,w)∈Z[q].We determine someμ(y,w)for y∈c_(0) and w∈c_(2),where c0 is the lowest two-sided cell of B_(2) and c_(2) is the higher one.Furthermore,we get some consequences using left or right strings and some properties of leading coefficients.
基金supported by National Natural Science Foundation of China (Grant No. 11501471)Fundamental Research Funds for the Central Universities (Grant No. 2682015BR017)
文摘The polynomial-like iterative equation is an important form of functional equations, in which iterates of the unknown function are linked in a linear combination. Most of known results were given for the given function to be monotone. We discuss this equation for continuous solutions in the case that the given function is a PM(piecewise monotone) function, a special class of non-monotonic functions. Using extension method, we give a general construction of solutions for the polynomial-like iterative equation.
