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Search: MSC category 22E35 ( Analysis on $p$-adic Lie groups )

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1. CMB 2006 (vol 49 pp. 578)

Muić, Goran
On the Structure of the Full Lift for the Howe Correspondence of $(Sp(n), O(V))$ for Rank-One Reducibilities
In this paper we determine the structure of the full lift for the Howe correspondence of $(Sp(n),O(V))$ for rank-one reducibilities.

Categories:22E35, 22E50, 11F70

2. CMB 2002 (vol 45 pp. 220)

Hakim, Jeffrey; Murnaghan, Fiona
Globalization of Distinguished Supercuspidal Representations of $\GL(n)$
An irreducible supercuspidal representation $\pi$ of $G= \GL(n,F)$, where $F$ is a nonarchimedean local field of characteristic zero, is said to be ``distinguished'' by a subgroup $H$ of $G$ and a quasicharacter $\chi$ of $H$ if $\Hom_H(\pi,\chi)\noteq 0$. There is a suitable global analogue of this notion for and irreducible, automorphic, cuspidal representation associated to $\GL(n)$. Under certain general hypotheses, it is shown in this paper that every distinguished, irreducible, supercuspidal representation may be realized as a local component of a distinguished, irreducible automorphic, cuspidal representation. Applications to the theory of distinguished supercuspidal representations are provided.

Categories:22E50, 22E35, 11F70

3. CMB 2001 (vol 44 pp. 482)

Mezo, Paul
Matching of Weighted Orbital Integrals for Metaplectic Correspondences
We prove an identity between weighted orbital integrals of the unit elements in the Hecke algebras of $\GL(r)$ and its $n$-fold metaplectic covering, under the assumption that $n$ is relatively prime to any proper divisor of every $1 \leq j \leq r$.

Category:22E35

4. CMB 2001 (vol 44 pp. 298)

Muić, Goran
A Proof of Casselman-Shahidi's Conjecture for Quasi-split Classical Groups
In this paper the author prove that standard modules of classical groups whose Langlands quotients are generic are irreducible. This establishes a conjecture of Casselman and Shahidi for this important class of groups.

Category:22E35

5. CMB 2000 (vol 43 pp. 380)

Shahidi, Freydoon
Twists of a General Class of $L$-Functions by Highly Ramified Characters
It is shown that given a local $L$-function defined by Langlands-Shahidi method, there exists a highly ramified character of the group which when is twisted with the original representation leads to a trivial $L$-function.

Categories:11F70, 22E35, 22E50

6. CMB 2000 (vol 43 pp. 90)

Muić, Goran; Savin, Gordan
Complementary Series for Hermitian Quaternionic Groups
Let $G$ be a hermitian quaternionic group. We determine complementary series for representations of $G$ induced from super-cuspidal representations of a Levi factor of the Siegel maximal parabolic subgroup of $G$.

Category:22E35

7. CMB 1999 (vol 42 pp. 393)

Savin, Gordan
A Class of Supercuspidal Representations of $G_2(k)$
Let $H$ be an exceptional, adjoint group of type $E_6$ and split rank 2, over a $p$-adic field $k$. In this article we discuss the restriction of the minimal representation of $H$ to a dual pair $\PD^{\times}\times G_2(k)$, where $D$ is a division algebra of dimension 9 over $k$. In particular, we discover an interesting class of supercuspidal representations of $G_2(k)$.

Categories:22E35, 22E50, 11F70

8. CMB 1997 (vol 40 pp. 376)

Gross, Benedict H.; Savin, Gordan
The dual pair $PGL_3 \times G_2$
Let $H$ be the split, adjoint group of type $E_6$ over a $p$-adic field. In this paper we study the restriction of the minimal representation of $H$ to the closed subgroup $PGL_3 \times G_2$.

Categories:22E35, and, 50, 11F70

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