Deligne–Lusztig Character

Given a connected reductive group $\mathbf{G}$ and an $F$-stable maximal torus $\mathbf{T}_w$ (parameterised by an element $w$ of the Weyl group $W$), the Deligne–Lusztig character $R_{\mathbf{T}_w}(1)$ is the virtual character of $\mathbf{G}(\mathbb{F}_q)$ obtained by $\ell$-adic cohomology of the Deligne–Lusztig variety associated to $w$. This tool expands $R_{\mathbf{T}_w}(1)$ in the basis of unipotent characters, displaying the integer inner products $\langle \gamma, R_{\mathbf{T}_w}(1)\rangle$ for each unipotent character $\gamma$. The torus $\mathbf{T}_w$ can be specified either by choosing a $\phi$-conjugacy class of $W$ from a drop-down list, or by typing a word in the Coxeter generators (with 1-based indices, separated by spaces).

Dynkin TypeABCDEFG

Rank

Characteristic02