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Weyl Group Multiple Dirichlet Series by Ben Brubaker, Daniel Bump, Solomon Friedberg

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Chapter Ten

Noncritical Resonances

We recall that a short pattern (6.2) is resonant at i if li+1 = bi. This property depends only on the associated prototype, so resonance is actually a property of prototypes. We also call a first (middle) row entry ai critical if it is equal to one of its four neighbors, which are li, li+1, bi and bi−1. We say that the resonance at i is critical if either ai or ai+1 is critical.

THEOREM 10.1 Suppose that Image is a strict pattern with no critical resonances; then Image is also strict with no critical resonances. Choose canonical ...

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