Related papers: Ramification of weak Arthur packets for p-adic gro…

We compute the characters of many supercuspidal representations of reductive p-adic groups. Specifically, we deal with representations that arise via Yu's construction from data satisfying a certain compactness condition. Each character is…

Canonical relativized cylindric set algebras are used to sharpen the relative representation theorem for weakly associative relation algebras, that every complete atomic weakly associative relation algebra is isomorphic with the…

Ordering permutations by containment of inversion sets yields a fascinating partial order on the symmetric group: the weak order. This partial order is, among other things, a semidistributive lattice. As a consequence, every permutation has…

A property of weak stationarity of a matrix valued differential form at superdensity points of its vanishing set is proved. This result is then applied in the context of the Maurer-Cartan equation.

In this paper, applying the intersection theory of local Arthur packets, for symplectic and split odd special orthogonal groups G_n, we give the first complete proof of the enhanced Shahidi conjecture on generic representations in local…

We extend the Kechris--Pestov--Todor\v{c}evi\'c correspondence to weak Fra\"{\i}ss\'{e} categories and automorphism groups of generic objects. The new ingredient is the weak Ramsey property. We demonstrate the theory on several examples…

We present a new interpretation for reduced density matrices of secondary variables in relativistic systems via an analysis of Wigner's method to construct the irreducible unitary representations of the Poincar\'e group. We argue that the…

We describe boundedness and compactness properties for the operators obtained by the Weyl-Pedersen calculus in the case of the irreducible unitary representations of nilpotent Lie groups that are associated with flat coadjoint orbits. We…

We introduce a new extragradient iterative process, motivated and inspired by [S. H. Khan, A Picard-Mann Hybrid Iterative Process, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2013-69], for finding a common element of the set…

We establish a connection between certain unique models, or equivalently unique functionals, for representations of p-adic groups and linear characters of their corresponding Hecke algebras. This allows us to give a uniform evaluation of…

We use geometry of the wonderful compactification to obtain a new proof of the relation between Deligne-Lusztig (or Alvis-Curtis) duality for $p$-adic groups and the homological duality. This provides a new way to introduce an involution on…

Let F be a non-archimedean local field and let G be a connected reductive group defined over F. We assume that G splits over a tame extension of F and that the residual characteristic p does not divide the order of the Weyl group. To each…

Geometry of buildings is used to prove some homological properties of the category of smooth representations of a reductive p-adic group (Kazhdan's "pairing conjecture", Bernstein's description of homological duality in terms of…

We present the Mathematica application LieART (Lie Algebras and Representation Theory) for computations frequently encountered in Lie Algebras and representation theory, such as tensor product decomposition and subalgebra branching of…

We develop a general procedure to study the combinatorial structure of Arthur packets for $p$-adic quasisplit $Sp(N)$ and $O(N)$ following the works of M{\oe}glin. This allows us to answer many delicate questions concerning the Arthur…

In this paper we study certain category of smooth modules for reductive $p$--adic groups analogous to the usual smooth complex representations but with the field of complex numbers replaced by a $\mathbb Q$--algebra. We prove some…

The goal of this paper is to remove the irreducibility hypothesis in a theorem of Richard Taylor describing the image of complex conjugations by $p$-adic Galois representations associated with regular, algebraic, essentially self-dual,…

In this note, we use give some algebraic applications of a previous result by the author which compares the deformations parameterized by the Maurer-Cartan elements of a differential graded Lie algebra, and a differential graded Lie…

Let G be a connected reductive complex affine algebraic group, and let X denote the moduli space of G-valued representations of a rank r free group. We first characterize the singularities in X, extending a theorem of Richardson and proving…

We consider the symplectic group $\mathrm{Sp}_{2n}$ defined over a $p$-adic field $F$, where $p=2$. We prove that every simple supercuspidal representation (in the sense of Gross--Reeder) of $\mathrm{Sp}_{2n}(F)$ corresponds to an…