In a recent paper, Pukanszky [6] has classified all the irreducible unitary representations of the universal covering group G of Gi = SL(2, R). We construct analytic continuations of the "principal series" of representations of G into certain domains in the complex plane. The representations obtained by continuation are uniformly bounded and, in special cases, they are equivalent to those const...

I give an algorithm for computing the full space of automorphic forms for definite unitary groups over Q, and apply this to calculate the automorphic forms of level G(Ẑ) and various small weights for an example of a rank 3 unitary group. This leads to some examples of various types of endoscopic lifting from automorphic forms for U1 × U1 × U1 and U1 × U2, and to an example of a non-endoscopic f...

Abstract We consider the irreducible representations each of dimension 2 necklace braid group $${\mathcal {N}}{\mathcal {B}}_n$$ N B n ( $$n=2,3,4$$ = 2 , 3 <mml:...

This paper gives a criterion for the non-vanishing of Dirac cohomology $\mathcal{L}_S(Z)$, where $\mathcal{L}_S(\cdot)$ is cohomological induction functor, while inducing module $Z$ irreducible, unitarizable, and in good range. As an application, we give formula counting number strings series. Using this formula, classify all irreducible unitary representations $E_{6(2)}$ with non-zero cohomolo...

We give a complete description of the discrete spectra in branching law $\Pi|_{G'}$ with respect to pair $(G,G')=(O(p,q), O(p',q') \times O(p'',q''))$ for irreducible unitary representations $\Pi$ $G$ that are "geometric quantization" minimal elliptic coadjoint orbits. also construct explicitly all holographic operators and prove closed Parseval-type formula.

The orbit method conjectures a close relationship between the set of irreducible unitary representations of a Lie group G, and admissible coadjoint orbits in the dual of the Lie algebra. We define admissibility for nilpotent coadjoint orbits of p-adic reductive Lie groups, and compute the set of admissible orbits for a range of examples. We find that for unitary, symplectic, orthogonal, general...

Using the sharpened Helgason–Johnson bound, this paper classifies all irreducible unitary representations with non-zero Dirac cohomology of E7(−5). As an application, we find that cancellation between even part and odd continues to happen for certain Assuming infinitesimal character being integral, further improve bound This should help people understand (part of) dual group.

Let G be a connected and simply connected nilpotent Lie group with Lie algebra g and unitary dual Ĝ. The moment map for π ∈ Ĝ sends smooth vectors in the representation space of π to g∗. The closure of the image of the moment map for π is called its moment set. N. Wildberger has proved that the moment set for π coincides with the closure of the convex hull of the corresponding coadjoint orbit. ...