Date: 22 May 2012

Littelmann Patterns and Weyl Group Multiple Dirichlet Series of Type D

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Abstract

We formulate a conjecture for the local parts of Weyl group multiple Dirichlet series attached to root systems of type D. Our conjecture is analogous to the description of the local parts of type A series given by Brubaker et al. (Ann. of Math. 166(1):293–316, 2007) in terms of Gelfand–Tsetlin patterns. Our conjecture is given in terms of patterns for irreducible representations of even orthogonal Lie algebras developed by Littelmann (Transform. Groups 3(2):145–179, 1998).