Equivariant characteristic quasi-polynomials refine the standard ones via permutation characters on Coxeter arrangement complements, with explicit formulas computed for all irreducible reduced root systems.
Root systems constructed by folding of the extended Dynkin diagrams
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abstract
The extended affine Weyl group of a root system is the semidirect product of the corresponding Weyl group by its coweight lattice. The stabilizer subgroup of the extended affine Weyl group with respect to the corresponding fundamental alcove induces a subgroup of automorphisms of the extended Dynkin diagram. In this paper, we construct a finite root system by folding by the elements of the subgroup.
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2026 1verdicts
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Equivariant version of the characteristic quasi-polynomials of root systems
Equivariant characteristic quasi-polynomials refine the standard ones via permutation characters on Coxeter arrangement complements, with explicit formulas computed for all irreducible reduced root systems.