Related papers: Theta Correspondence for U(1,1) and U(2)
Let F be a non-archimedean local field of odd residual characteristic. Let G be a (connected) reductive group over F that splits over a tamely ramified field extension of F. We revisit Yu's construction of smooth complex representations of…
Using exceptional theta correspondences, we prove that certain Weil representations of $p$-adic groups are multiplicity free and determine irreducible quotients.
In this paper we compute the multiplicities appearing in the ${\overline{\mathbb{F}}_\ell}$-modular theta correspondence in type II over a non-archimedean field $\mathrm{F}$, where $\ell$ is a prime not dividing the residue cardinality of…
We first discuss the relationship between the SL(2;R)/U(1) supercoset and N=2 Liouville theory and make a precise correspondence between their representations. We shall show that the discrete unitary representations of SL(2;R)/U(1) theory…
To a finite quadratic module, that is, a finite abelian group D together with a non-singular quadratic form Q:D --> Q/Z, it is possible to associate a representation of either the modular group, SL(2,Z), or its metaplectic cover, Mp(2,Z),…
Given a 2-stranded tangle in a $\ZZ/2$ homology ball, $T\subset Y$, we investigate the character variety $R(Y,T)$ of conjugacy classes of traceless SU(2) representations of $\pi_1(Y\setminus T)$. In particular we completely determine the…
Suppose G is a real reductive Lie group in Harish-Chandra's class. We propose here a structure for the set \Pi_u(G) of equivalence classes of irreducible unitary representations of G. (The subscript u will be used throughout to indicate…
We study a problem concerning parabolic induction in certain p-adic unitary groups. More precisely, for $E/F$ a quadratic extension of p-adic fields the associated unitary group $G=\mathrm{U}(n,n)$ contains a parabolic subgroup $P$ with…
We consider polynomial deformations of Lie superalgebras and their representations. For the class A(n-1,0) ~ sl(n/1), we identify families of superalgebras of quadratic and cubic type, consistent with Jacobi identities. For such deformed…
This paper surveys what is known about (conjectural) $p$-adic and $p$-modular semisimple Langlands correspondences in the non-supercuspidal setting for the unramified quasi-split unitary group…
We describe the twisted affine superalgebra $sl(2|2)^{(2)}$ and its quantized version $U_q[sl(2|2)^{(2)}]$. We investigate the tensor product representation of the 4-dimensional grade star representation for the fixed point subsuperalgebra…
The three dimensional U(1) Lattice Gauge, in the weak coupling limit, is dual to a Discrete Gaussian model. We investigate this dual model and use it to calculate properties of the U(1) theory. We find that, because of the nature of the…
Following the approach of B. Roberts, we characterize the non-vanishing of global theta lifts for symplectic-orthogonal dual pairs in terms of its local counterpart. In particular, we replace the temperedness assumption present in Robert's…
In this paper, we investigate the local Gan-Gross-Prasad conjecture for some pair of representations of $U(3)\times U(2)$ involving a non-generic representation. For a pair of generic $L$-parameters of $(U(n),U(n-1))$, it is known that…
We provide formulas for the denominator and superdenominator of a basic classical type Lie superalgebra for any set of positive roots. We establish a connection between certain sets of positive roots and the theory of reductive dual pairs…
We construct the local Langlands correspondence of essentially unipotent supercuspidal representations under the framework of rigid inner forms and prove a certaion functoriality and compatibilities. This result is stronger than the…
We propose a geometric strategy of giving explicit description of the Langlands parameter of an irreducible supercuspidal representation of GL(n) over a non-archimedean local field. The key is to compare the cohomology of an affinoid in the…
We establish a Siegel-Weil formula for the dual pair $(U(1,1), U(V))$ over a function field, where $V$ is a hermitian space of dimension greater than 2.
Mumford's well-known characterization of the hyperelliptic locus of the moduli space of ppavs in terms of vanishing and non-vanishing theta constants is based on Neumann's dynamical system. Poor's approach to the characterization uses the…
In this paper we obtain the orthogonality relations for the supergroup U(m|n), which are remarkably different from the ones for the U(N) case. We extend our results for ordinary representations, obtained some time ago, to the case of…