Related papers: The Sato-Tate law for Drinfeld modules

Let $\phi$ be a rank $r$ Drinfeld $\BF_q[T]$-module determined by $\phi_T(X) = TX+g_1X^q+...+g_{r-1}X^{q^{r-1}}+X^{q^r}$, where $g_1,...,g_{r-1}$ are algebraically independent over $\BF_q(T)$. Let $N\in\BF_q[T]$ be a polynomial, and…

With a fixed prime power $q>1$, define the ring of polynomials $A=\mathbb{F}_q[t]$ and its fraction field $F=\mathbb{F}_q(t)$. For each pair $a=(a_1,a_2) \in A^2$ with $a_2$ nonzero, let $\phi(a)\colon A\to F\{\tau\}$ be the Drinfeld…

The main goal of this paper is to generalize Serre-Tate theory of "ordinary" local moduli to Shimura varieties of PEL type. To this end we develop a generalized notion of ordinariness, we prove a number of basic results about this, and we…

The Lie superalgebra $W(\infty)$ is defined to be the direct limit of the simple finite-dimensional Cartan type Lie superalgebras $W(n)$ as $n$ goes to infinity, where $W(n)$ denotes the Lie superalgebra of superderivations of the Grassmann…

We study the behavior of the Iwasawa invariants of the Iwasawa modules which appear in Kato's main conjecture without $p$-adic $L$-functions under congruences. It generalizes the work of Greenberg-Vatsal, Emerton-Pollack-Weston, B.D. Kim,…

We introduce the notion of Drinfeld modular forms with $A$-expansions, where instead of the usual Fourier expansion in $t^n$ ($t$ being the uniformizer at `infinity'), parametrized by $n \in \mathbb{N}$, we look at expansions in $t_a$,…

We generalize some results of Greither and Popescu to a geometric Galois cover $X\rightarrow Y$ which appears naturally for example in extensions generated by $\mathfrak{p}^n$-torsion points of a rank 1 normalized Drinfeld module (i.e. in…

In the present paper, we introduce the notion of nearly holomorphic Drinfeld modular forms and study an analogue of Maass-Shimura operators in this context. Furthermore, for a given nearly holomorphic Drinfeld modular form, we show that its…

Let $\mathbb{F}_q[T]$ be the polynomial ring over a finite field $\mathbb{F}_q$. We study the endomorphism rings of Drinfeld $\mathbb{F}_q[T]$-modules of arbitrary rank over finite fields. We compare the endomorphism rings to their subrings…

We study certain family of finite-dimensional modules over the Yangian $Y(gl_N)$. The algebra $Y(gl_N)$ comes equipped with a distinguished maximal commutative subalgebra $A(gl_n)$ generated by the centres of all algebras in the chain…

In this paper, we show that total integrals and cointegrals are new sources of stable anti Yetter-Drinfeld modules. We explicitly show that how special types of total (co)integrals can be used to provide both (stable) anti Yetter-Drinfeld…

In this paper we aim to understand the category of stable-Yetter-Drinfeld modules over enveloping algebra of Lie algebras. To do so, we need to define such modules over Lie algebras. These two categories are shown to be isomorphic. A mixed…

Let $q$ be a prime power and $F=\mathbb{F}_q(T)$ be the rational function field over $\mathbb{F}_q$, the field with $q$ elements. Let $\phi$ be a Drinfeld module over $F$ and $\mathfrak{p}$ be a non-zero prime ideal of $A:=\mathbb{F}_q[T]$.…

Drinfeld orbifold algebras are a type of deformation of skew group algebras generalizing graded Hecke algebras of interest in representation theory, algebraic combinatorics, and noncommutative geometry. In this article, we classify all…

The Yang-Baxter equation (YBE) and the reflection equation (RE) both come from mathematical physics, and they can be defined in any monoidal category. For cartesian monoidal categories, we prove that every solution to the RE provides a…

In this paper we formulate a conjecture about the minimal dimensional representations of the finite $W$-superalgebra $U(\mathfrak{g}_\bbc,e)$ over the field of complex numbers and demonstrate it with examples including all the cases of type…

For the $p$-cyclotomic tower of $\mathbb{Q}_p$ Fontaine established a description of local Iwasawa cohomology with coefficients in a local Galois representation $V$ in terms of the $\psi$-operator acting on the attached etale…

The aim of this note is to prove various general properties of a generalization of the full module of first order differential operators on a commutative ring - a $\operatorname{D}$-Lie algebra. A $\operatorname{D}$-Lie algebra $\tilde{L}$…

We prove that the groups PSL(r,q^d) can be realized F_q(T)-regularly as Galois groups over the purely transcendental field F_q(T)(t_1,...,t_{r-1}) if r is even and r/2 is coprime to q^d-1. The method is to use twisted moduli schemes of…

We define a notion of pseudo-unitarizability for weight modules over a generalized Weyl algebra (of rank one, with commutative coeffiecient ring $R$), which is assumed to carry an involution of the form $X^*=Y$, $R^*\subseteq R$. We prove…