ICC Table

Displays the matrix of intersection-cohomology multiplicity polynomials $P_{X_i,\,L_j}(q)$ for a chosen Springer series, corresponding to ICCTable(uc, W) in GAP3/Chevie. The rows are indexed by character sheaves $X_i$ and the columns by local systems $L_j$ on unipotent classes; both are ordered by increasing $\dim B_u$. The entry $P_{X_i,\,L_j}(q)$ is the polynomial whose value at a prime power $q$ gives the multiplicity of the simple perverse sheaf $\mathrm{IC}(\bar{\mathcal{O}}_i, \mathcal{L}_i)$ in the decomposition of $j_!(\mathcal{L}_j)$. Diagonal entries are $1$ and entries below the diagonal (with respect to the closure order) are $0$.

Dynkin TypeABCDEFG

Rank

Characteristic02