Notation

One meaning per symbol; the source conventions are explained where they are used.

1 · Symbols

Table 1. Notation and definitions.
SymbolMeaningDefinition
\(\Loc\)Local fieldDefinition →
\(\Ring\)Valuation ringDefinition →
\(\unif\)UniformizerDefinition →
\(\resq\)Residue cardinalityDefinition →
\(\nDim\)Dimension, at least 2 in the modelDefinition →
\(\Grp\)Split reductive group; GLₙ in the modelDefinition →
\(\Iw\)Iwahori subgroupDefinition →
\(\shift\)One-step lattice shiftDefinition →
\(\idx\)Integer lattice indexDefinition →
\(\period\)Integer number of complete periodsDefinition →
\(\resid\)Remainder between 0 and n−1Definition →
\(\Lat\)Periodic lattices, with an indexDefinition →
\(\Wext\)Extended affine Weyl groupDefinition →
\(\Waff\)Affine reflection groupDefinition →
\(\Om\)Length-zero subgroupDefinition →
\(\len\)Affine lengthDefinition →
\(\alc\)Base alcoveDefinition →
\(\Hecke\)Iwahori–Hecke algebraDefinition →
\(\degdet\)Determinant-valuation mapDefinition →
\(\Module\)Iwahori-invariant Schwartz spaceDefinition →
\(\basic\)Basic function; indicator of L₀ in the modelDefinition →
\(\basisLat\)Lattice indicator, with an indexDefinition →
\(\basisShell\)Shell indicator, with an indexDefinition →
\(\Window\)Finite window of functions, with endpointsDefinition →
\(\lo\)Lower endpoint of a lattice windowDefinition →
\(\hi\)Upper endpoint of a lattice windowDefinition →
\(\Simple\)Simple perverse object, with an index in the modelDefinition →
\(\Category\)Geometric Iwahori-equivariant categoryDefinition →
\(\BasicSheaf\)Chosen basic sheafDefinition →
\(\HeckeAff\)Affine reflection subalgebraDefinition →
\(\LevelModule{\nu}\)Function space at level νDefinition →
\(\BaseGroup\)GL₂ in the symmetric group counterexampleDefinition →
\(\BaseIwahori\)Iwahori of G₀Definition →
\(\MaxCompact\)Maximal compact subgroup of G₀Definition →
\(\GroupHecke\)Iwahori–Hecke algebra of G₀Definition →
\(\signchar\)Sign character of the group Hecke algebraDefinition →