Between Dec 19, 2024 and Jan 2, 2025, datasets can be submitted to DRUM but will not be processed until after the break. Staff will not be available to answer email during this period, and will not be able to provide DOIs until after Jan 2. If you are in need of a DOI during this period, consider Dryad or OpenICPSR. Submission responses to the UDC may also be delayed during this time.

Browsing by Author "Gray, Nathan"

Now showing 1 - 1 of 1
  • Thumbnail Image
    Item
    Metaplectic Ice for Cartan Type C
    (2017-05) Gray, Nathan
    We use techniques from statistical mechanics to give evidence for new formulas for nonarchimedean metaplectic Whittaker functions, arising in the local theory of automorphic forms. We study a particular variation/generalization of the six-vertex model of type C having domain-wall boundary conditions dependent on a given integer partition $\lambda$ of length at most $r$, where $r$ is a fixed positive integer. More precisely, we examine a planar, non-nested, U-turn model whose partition function $Z_{\lambda}$ is related to characters of the symplectic group $\operatorname{Sp} (2r, \mathbb{C})$. We relate certain admissible states of our statistical-mechanical model to metaplectic Eisenstein series (or equivalently metaplectic Whittaker functions). We give a solution to the Yang--Baxter equation for metaplectic Boltzmann weights, which we use to derive two functional equations involving $Z_{\lambda}$, where one equation describes the action on $Z_{\lambda}$ by a short simple root, while the other describes the action by a long simple root. Finally, we give evidence for the conjecture that $Z_{\lambda}$ is a spherical Whittaker function by showing that $Z_{\lambda}$ satisfies the same identities under our solution to the Yang--Baxter equation as the metaplectic Whittaker function under intertwining operators on the unramified principal series of an $n$-fold metaplectic cover of $\operatorname{SO}(2r+1)$, for $n$ odd.