Related papers: The diagonal $p$-permutation functor $kR_k$

In a recent work of Galatius and Venkatesh, the authors showed the importance of studying simplicial generalizations of Galois deformation functors. They established a precise link between the simplicial universal deformation ring $R$…

We use $p$-component fermions $(p=2,3,...)$ to present $(2p-2)N$-fold integrals as a fermionic expectation value. This yields fermionic representation for various $(2p-2)$-matrix models. Links with the $p$-component KP hierarchy and also…

We study the permutation group $\mathcal{BK}_P$ generated by Bender-Knuth moves on linear extensions of a poset $P$, an analog of the Berenstein-Kirillov group on column-strict tableaux. We explore the group relations, with an emphasis on…

In this paper, we use techniques of Conrey, Farmer and Wallace to find spaces of modular forms $S_k(\Gamma_0(N))$ where all of the eigenspaces have Hecke eigenvalues defined over $\F_p$, and give a heuristic indicating that these are all…

Let p and q be two positive primes. In this paper we obtain a complete characterization of quaternion division algebras H_K(p,q) over the composite K of n quadratic number fields. Also, in Section 6, we obtain a characterization of…

Permutation polynomials with explicit constructions over finite fields have long been a topic of great interest in number theory. In recent years, by applying linear translators of functions from $\mathbb{F}_{q^n}$ to $\mathbb{F}_q$, many…

The goal of this paper is to give a numerical criterion for an open question in $p$-adic Fourier theory. Let $F$ be a finite extension of $\mathbf{Q}_p$. Schneider and Teitelbaum defined and studied the character variety $\mathfrak{X}$,…

Generalising the concept of a complete permutation polynomial over a finite field, we define completness to level $k$ for $k\ge1$ in fields of odd characteristic. We construct two families of polynomials that satisfy the condition of high…

We show that a new unitary transform with characteristics almost similar to those of the finite Fourier transform can be defined in any finite-dimensional Hilbert space. It is defined by using the Kravchuk polynomials, and we call it…

Let G be GL_N or SL_N as reductive linear algebraic group over a field k of positive characteristic p. We prove several results that were previously established only when N < 6 or p > 2^N. Let G act rationally on a finitely generated…

For a homomorphism f: A --> B of commutative rings, let D(A,B) denote Ker[Pic(A) --> Pic(B)]. Let k be a field and assume that A is a f.g. k-algebra. We prove a number of finiteness results for D(A,B). Here are four of them. 1: Suppose B is…

For the group of endo-permutation modules of a finite \(p\)-group, there is a surjective reduction modulo \(p\) homomorphism from a complete discrete valuation ring of characteristic 0 to its residue field of characteristic \(p\). We prove…

Tambara functors arise in equivariant homotopy theory as the structure adherent to the homotopy groups of a coherently commutative equivariant ring spectrum. We show that if $k$ is a field-like $C_{p^n}$-Tambara functor, then $k$ is the…

Let $p$ be a prime and let $G$ be a finite $p$-group. We show that the isomorphism type of the maximal abelian direct factor of $G$, as well as the isomorphism type of the group algebra over $\mathbb F_p$ of the non-abelian remaining direct…

An exact approach for the factorization of the relativistic linear singular oscillator is proposed. This model is expressed by the finite-difference Schr\"odinger-like equation. We have found finite-difference raising and lowering…

We study the ramification groups of finite Galois extensions $L/K$ of a complete discrete valuation field $K$ of equal characteristic $p>0$ with perfect residue field and Galois group isomorphic to the group of unitriangular matrices…

Following recent work of R. Cluckers and F. Loeser [Fonctions constructible et integration motivic I, C. R. Math. Acad. Sci. Paris 339 (2004) 411 - 416] on motivic integration, we develop a direct image formalism for positive constructible…

The k-th Fitting ideal of the Alexander invariant B of an arrangement A of n complex hyperplanes defines a characteristic subvariety, V_k(A), of the complex algebraic n-torus. In the combinatorially determined case where B decomposes as a…

For $G$ a symplectic or orthogonal $p$-adic group (not necessarily split), or an inner form of a general linear $p$-adic group, we compute the endomorphism algebras of some induced projective generators \`a la Bernstein of the category of…

Let $K$ be a local field of characteristic $p$ and let $L/K$ be a totally ramified elementary abelian $p$-extension with a single ramification break $b$. Byott and Elder defined the refined ramification breaks of $L/K$, an extension of the…