arXiv subjects

X. Griffin Wang

Publications and source records attributed to X. Griffin Wang.

3 recordsLinked to original sources

arXiv2026

The Tetrahedral (or $6j$) Symbol

We will attach a scalar invariant to a tetrahedron whose edges are labelled by irreducible representations of a ternary orthogonal group $\mathrm{SO}_3$ over a local field. This generalizes the $6j$ symbol whose theory was developed by Racah, Wigner, and Regge. We give several formulas for this invariant, including in terms of hypergeometric-type integrals and functions, and show that it admits a symmetry by the the $23040$-element Weyl group of $\mathrm{Spin}_{12}$. We then interpret these results in terms of relative Langlands duality, where the dual story comes from the action of $\mathrm{Spin}_{12}$ on a $16$-dimensional cone of spinors.

math.NT↗

arXiv2026

Relative Fundamental Lemmas for Spherical Hecke Algebras and Multiplicative Hitchin Fibrations: the Jacquet--Rallis Case

We prove the Jacquet--Rallis fundamental lemma for spherical Hecke algebras over local function fields using multiplicative Hitchin fibrations. Our work is inspired by the proof of [Yun11] in the Lie algebra case and builds upon the general framework of multiplicative Hitchin fibrations in [Wang26].

math.AG↗

arXiv2025

Multiplicative Hitchin Fibrations and the Fundamental Lemma

Let $k$ be a finite field and let $G$ be a reductive group over $k[[π]]$. Suppose $\mathrm{char}(k)$ is larger than twice the Coxeter number of $G$, we prove the standard endoscopic fundamental lemma for the spherical Hecke algebra of $G$ using multiplicative Hitchin fibrations.

math.AG↗