arXiv subjects
Publications and source records attributed to Nhat Hoang Le.
In this paper, we study the twisted Gan-Gross-Prasad problem for classical groups over finite fields. We formulate a multiplicity formula for Deligne-Lusztig characters and give a complete answer for cuspidal representations arising from elliptic tori.
In this paper, we study the Sakellaridis-Venkatesh conjecture for the rank-1 spherical variety $X=\text{Spin}_9\backslash F_4$ using an exceptional theta correspondence. We establish the correct transfer map satisfying relative character identities in this case and show that our transfer map agrees with the formula in (Sakellaridis, 2021). We also formulate the local relative characters for the degenerate Whittaker period of (Mao-Wan-Zhang, 2026a) associated with $X$. Moreover, we show how our techniques lead to a characterization of $X$-relatively cuspidal representations.
In this paper, we obtain geometric expansions of a local trace formula and its twisted variant for the twisted Gan-Gross-Prasad conjecture. As an application, we prove the local twisted Gan-Gross-Prasad conjecture for $U(V_K)/U(V)$ for tempered $L$-parameters over nonarchimedean fields of odd residual characteristic.
In this paper, following the method developed by J.-L. Waldspurger and R. Beuzart-Plessis for Bessel models, we study two local relative trace formulas for the local twisted Gan-Gross-Prasad conjecture. By obtaining spectral expansions and a partial geometric comparision between the two formulas, we prove the local twisted Gan-Gross-Prasad conjecture for $\text{GL(V)/U(V)}$ over nonarchimedean fields for tempered representations.