# Tagged Questions

**2**

votes

**2**answers

346 views

### Around the socle filtration of a Verma module

Work in the context of a finite dimensional simple Lie algebra over $\mathbb{C}$.
Write $W$ for the Weyl group and $\leq$ for the Bruhat order. For $w\in W$ let $\Delta_w$ denote the Verma module of ...

**34**

votes

**1**answer

870 views

### Implications of non-negativity of coefficients of arbitrary Kazhdan-Lusztig polynomials?

In their seminal 1979 paper here,
Kazhdan and Lusztig studied an arbitrary Coxeter group $(W,S)$ and the corresponding Iwahori-Hecke algebra. In particular they showed how to pass from a standard ...