Related papers: Arithmetic Satake compactifications and algebraic …

The $p\times p$ matrix version of the $r$-KdV hierarchy has been recently treated as the reduced system arising in a Drinfeld-Sokolov type Hamiltonian symmetry reduction applied to a Poisson submanifold in the dual of the Lie algebra…

If A is a cocommutative algebra with coproduct, then so is the smash product algebra of a symmetric algebra Sym(V) with A, where V is an A-module. Such smash product algebras, with A a group ring or a Lie algebra, have families of…

Suppose that G is a connected reductive group over a p-adic field F, that K is a hyperspecial maximal compact subgroup of G(F), and that V is an irreducible representation of K over the algebraic closure of the residue field of F. We…

We define uniformly the notions of Dirac operators and Dirac cohomology in the framework of the Hecke algebras introduced by Drinfeld. We generalize in this way the Dirac cohomology theory for Lusztig's graded affine Hecke algebras. We…

This paper considers a tiny modification of Justin Campbell's construction of the Kontsevich compactification in arXiv:1606.01518 [math.AG]. We construct a resolution of singularities of Drinfeld compactification with an Iwahori structure…

We address some questions posed by Goss related to the modularity of Drinfeld modules of rank 1 defined over the field of rational functions in one variable with coefficients in a finite field. For each positive characteristic valued…

We aim to provide a family of Drinfeld-Hecke eigenforms given in terms of a determinant of twisted Eisenstein series. Our main tool is the theory of vectorial Drinfeld modular forms, previously introduced by Pellarin [18] and extensively…

We introduce and study a natural class of Anderson t- modules, called triangular t-modules, characterized by having Drinfeld modules as their $\tau$-composition factors. They form a homologically meaningful generalization of Drinfeld…

For each Drinfeld-Sokolov integrable hierarchy associated to affine Kac-Moody algebra, we obtain a uniform construction of tau function by using tau-symmetric Hamiltonian densities, moreover, we represent its Virasoro symmetries as…

We equip the type $A$ diagrammatic Hecke category with a special derivation, so that after specialization to characteristic $p$ it becomes a $p$-dg category. We prove that the defining relations of the Hecke algebra are satisfied in the…

The Satake compactification of the moduli space of principally polarized abelian surfaces with a level two structure has a degree 8 endomorphism. The aim of this paper is to show that this result can be extended to other modular threefolds.…

The universal centralizer of a semisimple algebraic group is the family of centralizers of regular elements, parametrized by their conjugacy classes. When the group is of adjoint type, we construct a smooth, log-symplectic fiberwise…

We present an algorithm for computing the structure of any submodule of the module of points of a Drinfeld $A$-module over a finite field, where $A$ is a function ring over $\mathbb F_q$. When the function ring is $A = \mathbb F_q[T]$, we…

We derive sufficient conditions under which the ``second'' Hamiltonian structure of a class of generalized KdV-hierarchies defines one of the classical $\cal W$-algebras obtained through Drinfel'd-Sokolov Hamiltonian reduction. These…

We study the local factor at p of the semi-simple zeta function of a Shimura variety of Drinfeld type for a level structure given at p by the pro-unipotent radical of an Iwahori subgroup. Our method is an adaptation to this case of the…

Let $G$ be a reductive complex algebraic group. We fix a pair of opposite Borel subgroups and consider the corresponding semiinfinite orbits in the affine Grassmannian $Gr_G$. We prove Simon Schieder's conjecture identifying his bialgebra…

For a possibly twisted loop group $LG$, and any character sheaf of its Iwahori subgroup, we identify the associated affine Hecke category with a combinatorial category of Soergel bimodules. In fact, we prove such results for affine Hecke…

We recall first the analytic theory of the Hilbert modular varieties of level $\Gamma_1(\mathfrak{c},\mathfrak{n})$ and their compactifications. We construct arithmetic toroidal compactifications of the universal Hilbert-Blumenthal abelian…

We define the canonical submodule of a Drinfeld module of rank greater than one over the affine line over a finite field. (This extends the definition of the level 1 canonical subgroup of Hattori for rank 2 with ordinary reduction.) We give…

In this paper we present a systematic study of $W$ algebras from the Hamiltonian reduction point of view. The Drinfeld-Sokolov (DS) reduction scheme is generalized to arbitrary $sl_2$ embeddings thus showing that a large class of W algebras…