Related papers: Distinguished theta representations for certain co…

We study the dimension of the space of Whittaker functionals for depth zero representations of covering groups. In particular, we determine such dimensions for arbitrary Brylinski-Deligne coverings of the general linear group. The results…

For a Brylinski-Deligne covering group of a general linear group, we calculate some values of unramified Whittaker functions for certain representations that are analogous to the theta representations.

We prove a formula for the dimension of Whittaker functionals of irreducible constituents of a regular unramified genuine principal series for covering groups. The formula explicitly relates such dimension to the Kazhdan-Lusztig…

We show that the theta representations on certain covers of general linear groups support certain types of unique functionals. The proof involves two types of Fourier coefficients. The first are semi-Whittaker coefficients, which generalize…

For a unitary unramified genuine principal series representation of a covering group, we study the associated R-group. We prove a formula relating the R-group to the dimension of the Whittaker space for the irreducible constituents of such…

Theta representations appear globally as the residues of Eisenstein series on covers of groups; their unramified local constituents may be characterized as subquotients of certain principal series. A cuspidal theta representation is one…

Whittaker functions are special functions that arise in $p$-adic number theory and representation theory. They may be defined on representations of reductive groups as well as their metaplectic covering groups: fascinatingly, many of their…

Let $\theta$ and $\theta'$ be a pair of exceptional representations in the sense of Kazhdan and Patterson [KP], of a metaplectic double cover of $GL_n$. The tensor $\theta\otimes\theta'$ is a (very large) representation of $GL_n$. We…

We classify globally irreducible representations of alternating groups and double covers of symmetric and alternating groups. In order to achieve this classification we also completely characterise irreducible representations of such groups…

We prove that the numbers of irreducible n-dimensional complex continuous representations of the special linear groups over p-adic integers grow slower than the square of n. We deduce that the abscissas of convergence of the representation…

S.-Y. Pan decomposes the uniform projection of the Weil representation of a finite symplectic-odd orthogonal dual pair, in terms of Deligne-Lusztig virtual characters, assuming that the order of the finite field is large enough. In this…

Theta series for exceptional groups have been suggested as a possible description of the eleven-dimensional quantum supermembrane. We present explicit formulae for these automorphic forms whenever the underlying Lie group $G$ is split (or…

We study the generalized theta lifting between the double covers of split special orthogonal groups, which uses the non-minimal theta representations constructed by Bump, Friedberg and Ginzburg. We focus on the theta liftings of non-generic…

We study the theta lifting for real unitary groups and completely determine the theta lifts of discrete series representations. In particular, we show that these theta lifts can be expressed as cohomologically induced representations in the…

The classical theta correspondence establishes a relationship between automorphic representations on special orthogonal groups and automorphic representations on symplectic groups or their double covers. This correspondence is achieved by…

We study the automorphic theta representation $\Theta_{2n}^{(r)}$ on the $r$-fold cover of the symplectic group $Sp_{2n}$. This representation is obtained from the residues of Eisenstein series on this group. If $r$ is odd, $n\le r <2n$,…

We study the theta lifting for real unitary groups and completely determine the theta lifts of tempered representations. In particular, we show that the theta lifts of (limits of) discrete series representations can be expressed as…

We study representations of GL(n) appearing as quotients of a tensor of exceptional representations, in the sense of Kazhdan and Patterson. Such representations are called distinguished. We characterize distinguished principal series…

We incorporate covers of quasisplit reductive groups into the Langlands program, defining an L-group associated to such a cover. We work with all covers that arise from extensions of quasisplit reductive groups by $\mathbf{K}_2$ -- the…

We revisit the local metaplectic correspondence previously constructed and studied by Flicker and Kazhdan. After restoring and generalizing some of their results, we get several interesting applications to the representation theory of a…