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

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Chapter Eleven

Types

We now divide the prototypes into much smaller units that we call types. We fix a top and bottom row, and therefore a cartoon. For each episode ε of the cartoon, we fix an integer kε. Then the set Image of all short Gelfand-Tsetlin patterns (6.2) with the given top and bottom rows such that for each ε

Image

is called a type. Thus two patterns are in the same type if and only if they have the same top and bottom rows (and hence the same cartoon), and if the sum of the first (middle) row elements in each episode is the same for both patterns. ...

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