Related papers: The SL(1,D)-distinction problem

We use the theta lifts between Mp(2) and PD to study the distinction problems for the pair (Mp(2,E), SL(2,F )), where E is a quadratic field extension over a nonarchimedean local field F of characteristic zero and D is a quaternion algebra.…

We use relations between the base change representations and theta lifts, to give a new proof to the local period problems of SL(2) over a nonarchimedean quadratic field extension E/F. Then we will verify the Prasad conjecture for SL(2).…

Let $D$ be a quaternion division algebra over a non-archimedean local field $F$ of characteristic zero. Let $E/F$ be a quadratic extension and $\rm{SL}_{n}^{*}(E) = {\rm{GL}}_{n}(E) \cap \rm{SL}_{n}(D)$. We study distinguished…

Let $E$ be a two-dimensional \'etale algebra over a non-Archimedean local field $K$ of characteristic zero. We show that the unitary group of a non-degenerate hermitian lattice over $E$ is generated by symmetries and rescaled Eichler…

Let $D$ be the quatenion division algebra over a non-Archimedean local field $F$ of characteristic zero and odd residual characterisitc. We show that an irreducible discrete series representation of $\mathrm{GL}_n(D)$ is…

We study the relationship between the arithmetic and the spectrum of the Laplacian for manifolds arising from congruent arithmetic subgroups of SL(1,D), where D is an indefinite quaternion division algebra defined over a number field F. We…

For a central division algebra $D$, we study a family of representations of $\mathrm{GL}_{k,D}$ (both locally and globally), which can be viewed as analogues of the Speh representations. Locally, we study unique models for these…

The Witt group of skew hermitian forms over a division algebra $D$ with symplectic involution is shown to be canonically isomorphic to the Witt group of symmetric bilinear forms over the Severi-Brauer variety of $D$ with values in a…

We use the relations between the base change representations, theta lifts and Whittaker model, to give a new proof to the period problems of $GL(2)$ over a quadratic local field extension $E/F.$ And we classify both local and global…

The powerful group theoretical formalism of potential algebras is extended to non-Hermitian Hamiltonians with real eigenvalues by complexifying so(2,1), thereby getting the complex algebra sl(2,\C) or $A_1$. This leads to new types of both…

Let $E/F$ be a quadratic extension of a non-Archimedian local field. Splitting of the 2-fold metaplectic cover of ${\rm Sp}_{2n}(F)$ when restricted to various subgroups of ${\rm Sp}_{2n}(F)$ plays an important role in application of the…

We introduce the symplectic group $\mathrm{Sp}_2(A,\sigma)$ over a noncommutative algebra $A$ with an anti-involution $\sigma$. We realize several classical Lie groups as $\mathrm{Sp}_2$ over various noncommutative algebras, which provides…

We study non-linear sigma models with N local supersymmetries in three space-time dimensions. For N=1 and 2 the target space of these models is Riemannian or Kahler, respectively. All N>2 theories are associated with Einstein spaces. For…

If $E/F$ is a quadratic extension $p$-adic fields, we first prove that the $\mathrm{SL}_n(F)$-distinguished representations inside a distinguished unitary L-packet of $\mathrm{SL}_n(E)$ are precisely those admitting a degenerate Whittaker…

For $E/F$ a quadratic extension of local fields, and $\pi$ an irreducible admissible generic representation of $SL_n(E)$, we calculate the dimension of $Hom_{SL_n(F)}[\pi,C]$ and relate it to fibers of the base change map corresponding to…

Quadratic descent of hermitian and skew hermitian forms over division algebras with involution of the first kind in arbitrary characteristic is investigated and a criterion, in terms of systems of quadratic forms, is obtained. A refined…

We study the algebraic framework in which one can define, in the manner of the theta correspondence, a correspondence between representations of two locally profinite groups $H_1$, $H_2$. In particular, we examine when and how such a…

We provide a complete classification of quaternionic skew-Hermitian symmetric spaces, namely symmetric spaces that admit a torsion-free ${\rm SO}^{*}(2n){\rm Sp}(1)$-structure for arbitrary $n>1$. Moreover, we prove that any homogeneous…

Let F be a p-adic field with p odd. Quadratic base change and theta-lifting are shown to be compatible for supercuspidal representations of SL(2,F). The argument involves the theory of types and the lattice model of the Weil representation.

The paper develops elementary linear algebra methods to compute the determinants of the tensor symmetrizations of quadratic and hermitian forms over fields of good characteristic. Explicit results are given for the partitions $(n)$,…