# Littelmann patterns and Weyl group multiple Dirichlet series of type D

## TL;DR

This paper proposes a conjecture relating Littelmann patterns to the local components of Weyl group multiple Dirichlet series for type D root systems, extending previous work on type A series.

## Contribution

It introduces a new conjecture connecting Littelmann patterns with Weyl group multiple Dirichlet series of type D, generalizing known results from type A.

## Key findings

- Conjecture formulated for local parts of type D series.
- Extension of Gelfand--Tsetlin pattern approach to type D.
- Framework based on irreducible representations of orthogonal Lie algebras.

## 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, Bump, Friedberg, and Hoffstein 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.