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Keywords Poset · Rational function identities · Valuation of cones · Lattice points · Affine semigroup ring · Hilbert series · Total residue · Root system · Weight lattice..

We give a representation of an elliptic Weyl group W (R) (= the Weyl group for an elliptic root system ∗) R) in terms of the elliptic Dynkin diagram Γ(R, G) for the elliptic

We define the elliptic Hecke algebras for arbitrary marked elliptic root systems in terms of the corresponding elliptic Dynkin diagrams and make a ‘dictionary’ between the elliptic

In this paper we study the properties of asymptotic root-counting measures for families of (nonstandard) polynomial eigenfunctions of exactly solvable lin- ear differential

Let G be a split reductive algebraic group over L. In what follows we assume that our prime number p is odd, if the root system Φ has irreducible components of type B, C or F 4, and

Macdonald in [11], and a proof of Macdonald’s identities for infinite families of root systems was given by D..

The most far reaching generalisation of the Artin primitive root conjecture was considered by Lenstra [292], in the context of his research on Euclidean number fields: Let K be a

It implies that if the initial (M, φ) is c log-convergent (resp. overconvergent), then Dwork’s unit root zeta function in the ordinary rank one case can be expressed in terms