Chapter

Multiple Dirichlet Series, L-functions and Automorphic Forms

Volume 300 of the series Progress in Mathematics pp 119-130

Date:

Littelmann Patterns and Weyl Group Multiple Dirichlet Series of Type D

  • Gautam ChintaAffiliated withDepartment of Mathematics, The City College of New York
  • , Paul E. GunnellsAffiliated withDepartment of Mathematics and Statistics, University of Massachusetts Email author 

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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).

Keywords

Weyl group multiple Dirichlet series Crystal graph Gelfand-Tsetlin pattern Littelmann pattern