Related papers: On Multiplicity Formula for Spherical Varieties

In this paper, we form a conjecture about the multiplicities of all the strongly tempered spherical varieties without Type N root for tempered representations. This generalizes the epsilon dichotomy conjectures of Gan-Gross-Prasad and…

We study local multiplicities associated to the so-called generalized Shalika models. By establishing a local trace formula for these kind of models, we are able to prove a multiplicity formula for discrete series. As a result, we can show…

We prove an integral formula computing multiplicities of square-integrable representations relative to Galois pairs over $p$-adic fields and we apply this formula to verify two consequences of a conjecture of Dipendra Prasad. One concerns…

We associate to any complete spherical variety $X$ a certain nonnegative rational number $\wp(X)$, which we conjecture to satisfy the inequality $\wp(X) \le \operatorname{dim} X - \operatorname{rank} X$ with equality holding if and only if…

Using the theory of spherical varieties and especially Frobenius splitting results for symmetric varieties, we give a type independent very short proof of Wahl's conjecture for cominuscule homogeneous spaces for all primes different from 2.

A general framework for the reduction of the equations defining classes of spherical varieties to (maybe infinite dimensional) grassmannians is proposed. This is applied to model varieties of type A, B and C; in particular a standard…

Following the method developed by Waldspurger and Beuzart-Plessis in their proof of the local Gan-Gross-Prasad conjecture, we are able to prove the multiplicity one theorem for the Ginzburg-Rallis model over the Vogan packets in the…

We consider the local Ginzburg-Rallis model over complex field. We show that the multiplicity is always 1 for a majority of the generic representations. We also have partial results on the real case for general generic representations. This…

We prove a conjecture by Kreiman and Lakshmibai on a combinatorial description of multiplicities of points on Schubert varieties in Graszmannians in terms of certain sets of reflections in the corresponding Weyl group. The proof is…

This paper is devoted to study multiplicity and regularity as well as to present some classifications of complex analytic sets. We present an equivalence for complex analytical sets, namely blow-spherical equivalence and we receive several…

We propose a model-theoretic structure for Shimura varieties and give necessary and sufficient conditions to obtain categoricity. We show that these conditions are directly related to important conjectures in number theory coming from…

We study Hilbert-Samuel multiplicity for points of Schubert varieties in the complete flag variety, by Groebner degenerations of the Kazhdan-Lusztig ideal. In the covexillary case, we give a positive combinatorial rule for multiplicity by…

We consider the local multiplicity problems of the analogy of the Ginzburg-Rallis model for the unitary group and the unitary similitude group cases. For the unitary similitude group case, by proving a local trace formula for the model, we…

This article proves a formula relating the multiplicity of an induced representation and that of the inducing datum for the Bessel and the Fourier-Jacobi models over Archimedean local fields by generalizing the approach of C. Moeglin and…

We study homological multiplicities of spherical varieties of reductive group $G$ over a $p$-adic field $F$. Based on Bernstein's decomposition of the category of smooth representations of a $p$-adic group, we introduce a sheaf that…

We suggest a combinatorial criterion for the smoothness of an arbitrary spherical variety using the classification of multiplicity-free spaces, generalizing an earlier result of Camus for spherical varieties of type $A$.

In this paper, by proving a simple local trace formula for real reductive groups, we prove a multiplicity formula of K-types for all irreducible representations of real reductive groups. This multiplicity formula expresses the K-characters…

We prove a formula which compares intersection numbers of conormal varieties of two projective varieties and their dual varieties. When one of them is linear, we can recover the usual Plucker formula for the degree of the dual variety. The…

We establish the analog for real homogeneous spherical varieties of the Scattering Theorem of Sakellaridis and Venkatesh (Periods and harmonic analysis on spherical varieties, Asterisque 396, (2017), Theorem 7.3.1) for p-adic wavefront…

Xue proved an equational refinement of the unitary Shimura curve case of the arithmetic Gan-Gross-Prasad conjecture via the Gross-Zagier formula for quaternionic Shimura curves. On the other hand, Rapoport, Smithling and Zhang posed a…