Metaplectic Whittaker functions and crystal bases

By Peter J. McNamara. 2009

84 citations recorded by the source corpus.

We study Whittaker functions on nonlinear coverings of simple algebraic groups over a nonarchimedean local field. We produce a recipe for expressing such a Whittaker function as a weighted sum over a crystal graph and show that in type A, these expressions agree with known formulae for the prime-power-supported coefficients of multiple Dirichlet series.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8cdf62366a5fbffbcf8f21de5a646cb9ceedde2d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Gautam Chinta
2. Daniel Bump
3. S. Friedberg
4. Ben Brubaker
5. Omer Offen
6. Peter J. McNamara

In Geometry and Topology

1. Peter J. McNamara
2. Gautam Chinta
3. S. Friedberg
4. Daniel Bump
5. Ben Brubaker
6. Omer Offen
7. Paul E. Gunnells

In Mathematical Physics

1. Gautam Chinta
2. Daniel Bump
3. S. Friedberg
4. Ben Brubaker
5. Peter J. McNamara
6. Omer Offen
7. Paul E. Gunnells

Citations in the corpus

• Weyl group multiple Dirichlet series, Eisenstein series and crystal bases (2011, methodology): “This follows by combining the work of Chinta and Offen [17] demonstrating that the pparts in [16] are p-adic metaplectic Whittaker functions in type A with the work of McNamara [28] demonstrating that the p-part definition presented in the next section is indeed a p-adic metaplectic Whittaker functi”
• The metaplectic Casselman-Shalika formula (2011, background): “The author has already written a proof in the case where G s ∼ = SL 2 ( E ) [Mc1, Theorem 6.4], so we will not repeat the argument here.”
• A metaplectic Casselman-Shalika formula for GLr (2013, methodology): “We now provide a brief description of McNamara’s work [23].”