arXiv subjects
Publications and source records attributed to Hirotaka Kakuhama.
In this paper, we formulate a conjecture that describes the local theta correspondences in terms of the local Langland correspondences for rigid inner twists, which contain the correspondences for quaternionic dual pairs. Moreover, we verify the conjecture holds in some specific cases.
In this paper, we determine a constant occurring in a local analogue of the Siegel-Weil formula, and describe the behavior of the formal degrees under the local theta correspondence for quaternionic dual pairs of almost equal rank over a non-Archimedean local field of characteristic $0$. As an application, we prove the formal degree conjecture of Hiraga-Ichino-Ikeda for the non-split inner forms of ${\rm Sp}_4$ and ${\rm GSp}_4$.
In this paper, we give a precise definition of an analytic $γ$-factor of an irreducible representation of a classical group over a local function field of odd characteristic so that it satisfies some notable properties which are enough to define it uniquely. We use the doubling method to define the $γ$-factor, and the main theorem extends works of Lapid-Rallis, Gan, Yamana, and the author to a classical group over a local function field of odd characteristic.
In this paper, we give a precise definition of the analytic $γ$-factors of irreducible representations of quaternionic unitary groups, which extends a work of Lapid-Rallis.