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

We describe the supercuspidal representations of Sp(4,F), for F a non-archimedean local field of residual characteristic different from 2, and determine which are generic.

We describe all Witt invariants of anti-hermitian forms over a quaternion algebra with its canonical involution, and in particular all Witt invariants of orthogonal groups $O(A,\sigma)$ where $(A,\sigma)$ is an central simple algebra with…

The families of quasi-simple or Cayley--Klein algebras associated to antihermitian matrices over R, C and H are described in a unified framework. These three families include simple and non-simple real Lie algebras which can be obtained by…

We analyse a class of non-Hermitian Hamiltonians, which can be expressed bilinearly in terms of generators of a sl(2,R)-Lie algebra or their isomorphic su(1,1)-counterparts. The Hamlitonians are prototypes for solvable models of Lie…

Linear complementary dual codes (LCD) intersect trivially with their dual. In this paper, we develop a new characterization for LCD codes, which allows us to judge the complementary duality of linear codes from the codeword level. Further,…

We give an explicit construction of all complex continuous irreducible characters of the group ${\rm SL}_1(D)$, where $D$ is a division algebra of prime degree $\ell$ over a local field of odd residual characteristic different than $\ell$.…

We study equivariant Hermitian K-theory for representations of symplectic groups, especially $\mathrm{SL}_2$. The results are used to establish an Atiyah-Segal completion theorem for Hermitian $K$-theory and symplectic groups.

We construct and study the holomorphic discrete series representation and the principal series representation of the symplectic group $\mathrm{Sp}(2n,F)$ over a $p$-adic field $F$ as well as a duality between some sub-representations of…

The product of a complex skew-symmetric matrix and its conjugate transpose is a positive semi-definite Hermitian matrix with nonnegative eigenvalues, with a property that each distinct positive eigenvalue has even multiplicity. This…

Some thoughts on the congruence D=0,1(mod 4) for the absolute discriminant D of a number field

The local Langlands correspondence for GL(n) of a non-Archimedean local field $F$ parametrizes irreducible admissible representations of $GL(n,F)$ in terms of representations of the Weil-Deligne group $WD_F$ of $F$. The correspondence,…

In this paper, we introduce the notion of incoherent definite orthogonal and Hermitian spaces, and use their neighboring spaces as a tool for the local study of orthogonal and unitary Shimura varieties. This generalizes earlier work, using…

We study a family of complex representations of the group GL(n,O), where O is the ring of integers of a non-archimedean local field F. These representations occur in the restriction of the Grassmann representation of GL(n,F) to its maximal…

Building on our previous work on rigid analytic uniformizations, we introduce Darmon points on Jacobians of Shimura curves attached to quaternion algebras over Q and formulate conjectures about their rationality properties. Moreover, if K…

The $N=2$ fermionic string theory is revisited in light of its recently proposed equivalence to the non-compact $N=4$ fermionic string model. The issues of space-time Lorentz covariance and supersymmetry for the BRST quantized $N=2$ strings…

We study relations between special elliptic isometries in the complex hyperbolic plane. Relations of lengths 2, 3, and 4 are fully classified. Some relative SU(2,1)-character varieties of the quadruply punctured sphere are described and…

We consider the non-supersymmetric "magic" theories based on the split quaternion and the split complex division algebras. We show that these theories arise as "Ehlers" $SL(2,\mathbb{R})$ and $SL(3,\mathbb{R})$ truncations of the maximal…

For a field k$with an automorphism \sigma and a derivation \delta, we introduce the notion of liouvillian solutions of linear difference-differential systems {\sigma(Y) = AY, \delta(Y) = BY} over k and characterize the existence of…

{\small In this paper, we find a class of division quaternion algebras over the field }$\mathbb{Q}\left( i\right) ${\small \ and a class of division symbol algebras over a cyclotomic field.}

We outline some recent developments in higher dimensional Quark-Lepton (QL) symmetric models. The QL symmetric model in five dimensions is discussed, with particular emphasis on the use of split fermions. An interesting fermionic geography…