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A holomorphic continuation of Jacquet type integrals for parabolic subgroups with abelian nilradical is studied. Complete results are given for generic characters with compact stabilizer and arbitrary representations induced from admissible representations. A description of all of the pertinent examples is given. These results give a complete description of the Bessel models corresponding to compact stabilizer.
Recently a remarkable map between 4-dimensional superconformal field theories and vertex algebras has been constructed cite{BLLPRV15}. This has lead to new insights in the theory of characters of vertex algebras. In particular it was observed that in
In his seminal Lecture Notes in Mathematics published in 1981, Andrey Zelevinsky introduced a new family of Hopf algebras which he called {em PSH-algebras}. These algebras were designed to capture the representation theory of the symmetric groups and
In this paper, we obtain stability results for martingale representations in a very general framework. More specifically, we consider a sequence of martingales each adapted to its own filtration, and a sequence of random variables measurable with res
The special linear representation of a compact Lie group G is a kind of linear representation of compact Lie group G with special properties. It is possible to define the integral of linear representation and extend this concept to special linear representation for next using.
Let $K/F$ be a quadratic extension of $p$-adic fields, $sigma$ the nontrivial element of the Galois group of $K$ over $F$, and $pi$ a quasi-square-integrable representation of $GL(n,K)$. Denoting by $pi^{vee}$ the smooth contragredient of $pi$, and b