Related papers: The endoscopic character identity for even special…

Even with the introduction of supercharacter theories, the representation theory of many unipotent groups remains mysterious. This paper constructs a family of supercharacter theories for normal pattern groups in a way that exhibit many of…

We discuss progress towards the classification of irreducible admissible representations of reductive groups over non-archimedean local fields and the local Langlands correspondence. We also state some (partly conjectural) compatibility…

We consider two variants of those Abelian groups with all proper characteristic subgroups isomorphic and give an in-depth study of their basic and specific properties in either parallel or contrast to the Abelian groups with all proper…

We study the relations governing the ring of quasiautomorphic forms associated to triangle groups with a single cusp, thereby extending our earlier results on Hecke groups. The Eisenstein series associated to these triangle groups are shown…

In this paper we construct explicitly a square integrable residual automorphic representation of the special orthogonal group $SO_{2n}$, through Eisenstein series. We show that this representation comes from an elliptic Arthur parameter…

The paper investigates a significant part of the automorphic, in fact of the so-called Eisenstein cohomology of split odd orthogonal groups over Q. The main result provides a description of residual and regular Eisenstein cohomology classes…

In this note we answer the question raised by D. Goss in [Applications of non-Archimedean integration to the $L$-series of $\tau$-sheaves, {\em J. Number Theory,} 110 (2005), no. 1, 83--113] by proving that the group of locally analytic…

This paper proves the local Langlands conjecture for the non quasi-split inner form Sp(1,1) of Sp(4) over a p-adic field of characteristic 0, by studying the restriction of representations from the non quasi-split inner form GSp(1,1) of…

Nonlocality is a quintessential signature of nonclassical behaviour and a resource for quantum advantages in communication and computation. The paradoxical correlations witnessed by strong nonlocality undergird the standard probabilistic…

Building on reduction theorems and dimension bounds for symmetric groups obtained in our earlier work, we classify the irreducible restrictions of representations of the symmetric and alternating groups to proper subgroups. Such…

We construct an endoscopic decomposition for local L-packets associated to irreducible cuspidal Deligne-Lusztig representations. Moreover, the obtained decomposition is compatible with inner twistings.

In this paper, following Arthur's ideas, we rework the process of constructing the anti-tempered local Arthur packets for quasi-split classical groups and their pure inner forms. In particular, we present explicit examples illustrating…

For any complex reductive group $G$ and any compact Riemann surface with genus $g>0$, we show that every connected component of the associated character variety is $\mathbb{Q}$-factorial and has symplectic singularities, and classify the…

Identities of complex irreducible representations of finite groups can be explicitly constructed from character value sets. Among other things, these identities determine representations up to Gassmann equivalency. Some examples of…

We consider a general version of the phenomenon of more nonlocality with less entanglement, within the framework of the unambiguous (i.e., conclusive) quantum state discrimination problem under local quantum operations and classical…

Using the natural irreducible 8-dimensional representation and the two spin representations of the quantum group $U_q$(D$_4$) of D$_4$, we construct a quantum analogue of the split octonions and study its properties. We prove that the…

We study the problem of classifying triangulated categories with finite-dimensional morphism spaces and finitely many indecomposables over an algebraically closed field. We obtain a new proof of the following result due to Xiao and Zhu: the…

Homogeneous compatible almost complex structures on symplectic manifolds are studied, focusing on those which are special, meaning that their Chern-Ricci form is a multiple of the symplectic form. Non Chern-Ricci flat ones are proven to be…

We complete the discrete cluster categories of type $\mathbb{A}$ as defined by Igusa and Todorov, by embedding such a discrete cluster category inside a larger one, and then taking a certain Verdier quotient. The resulting category is a…

We associate to every central simple algebra with involution of orthogonal type in characteristic two a totally singular quadratic form which reflects certain anisotropy properties of the involution. It is shown that this quadratic form can…