arXiv subjects

Liping Wang

Publications and source records attributed to Liping Wang.

92 records · Page 6Linked to original sources

arXiv2010

Some multiplication formulas in an affine Hecke algebra

In this paper we consider the Hecke algebra $\mathcal {H}$ associated to an extended affine Weyl group of type $\widetilde{B_2}$. We give some interesting formulas on $C_{rt}S_λ$, which imply some relations between the Kazhdan-Lusztig coefficients $μ(y,w)$ and representations of some algebraic groups. Here $C_{rt}$ is one element in the Kazhdan-Lusztig basis of $\mathcal {H}$ and $S_λ$ is an element in the center of $\mathcal {H}$.

math.RT↗

arXiv2010

Leading coefficients of the Kazhdan-Lusztig polynomials for an Affine Weyl group of type $\widetilde{B_2}$

In this paper we compute the leading coefficients $μ(u,w)$ of the Kazhdan--Lusztig polynomials $P_{u,w}$ for an affine Weyl group of type $\tilde{B}_2$. By using the \textbf{a}-function of a Coxeter group defined by Lusztig (see [L1, \S2]), we compute most $μ(u,w)$ explicitly. With part of these values $μ(u,w)$, we show that a conjecture of Lusztig on distinguished involutions is true for an affine Weyl group of type $\tilde{B}_2$. We also show that the conjectural formula in [L3, (12)] needs a modification.

math.CO↗