Related papers: On Drinfeld modular forms of higher rank IV: Modul…

Let $\fa$ be an ideal of a Noetherian local ring $R$ and let $C$ be a semidualizing $R$-module. For an $R$-module $X$, we denote any of the quantities $\fd_R X$, $\Gfd_R X$ and $\GCfd_RX$ by $\T(X)$. Let $M$ be an $R$-module such that…

A fundamental question, first raised by Langlands, is to know whether the Rankin-Selberg product of two (not necessarily holomorphic) cusp forms f and g is modular, i.e., if there exists an automorphic form f box g on GL(4)/Q whose standard…

Let G be a split connected reductive group over a finite field F_q, and N its maximal unipotent subgroup. V. Drinfeld has introduced a remarkable partial compactification of the moduli stack of N-bundles on a smooth projective curve X over…

In this paper, we try to answer the following question: given a modular tensor category $\A$ with an action of a compact group $G$, is it possible to describe in a suitable sense the ``quotient'' category $\A/G$? We give a full answer in…

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 show that all isomorphism classes of even rank Tambara-Yamagami categories arise as $\mathbb{Z}_2$-twisted representations of conformal nets. As a consequence, we show that their Drinfel'd centers are realized by (generalized) orbifolds…

Over an algebraically closed base field $k$ of characteristic 2, the ring $R^G$ of invariants is studied, $G$ being the orthogonal group O(n) or the special orthogonal group SO(n) and acting naturally on the coordinate ring $R$ of the…

For a regular normal element in an arbitrary ring, we study the category of its module factorizations. The cokernel functor relates module factorizations with Gorenstein projective components to Gorenstein projective modules over the…

Let $R$ be a Gorenstein local ring with maximal ideal $\mathfrak{m}$ satisfying $\mathfrak{m}^3=0\ne\mathfrak{m}^2$. Set $k=R/\mathfrak{m}$ and $e=\text{rank}_{k}(\mathfrak{m}/\mathfrak{m}^2)$. If $e>2$ and $M$, $N$ are finitely generated…

For a reductive group G, we study the Drinfeld-Gaitsgory functor of the category of conjugation-equivariant D-modules on G. We show that this functor is an equivalence of categories, and that it has a filtration with layers expressed via…

A set of nonlinear differential equations associated with the Eisenstein series of the congruent subgroup $\Gamma_0(2)$ of the modular group $SL_2(\mathbb{Z})$ is constructed. These nonlinear equations are analogues of the well known…

We rederive a popular nonsemisimple fusion algebra in the braided context, from a Nichols algebra. Together with the decomposition that we find for the product of simple Yetter-Drinfeld modules, this strongly suggests that the relevant…

Let $R$ be a commutative noetherian ring. The $n$-semidualizing modules of $R$ are generalizations of its semidualizing modules. We will prove some basic properties of $n$-semidualizing modules. Our main result and example shows that the…

We explicitly determine the group of isomorphism classes of equivariant line bundles on the non-archimedean Drinfeld upper half plane for $\mathrm{GL}_2(F)$, for its subgroups of matrices whose determinant has even (respectively trivial)…

In this paper, the authors apply a stratification of moduli spaces of complex Lie algebras to analyzing the moduli spaces of nxn matrices under scalar similarity and bilinear forms under the cogredient action. For similar matrices, we give…

Let $(A,\m)$ be a Noetherian local ring, let $M$ be a finitely generated \CM $A$-module of dimension $r \geq 2$ and let $I$ be an ideal of definition for $M$. Set $L^I(M) = \bigoplus_{n\geq 0}M/I^{n+1}M$. In part one of this paper we showed…

The aim of this paper is to construct an immersion of the Drinfeld moduli schemes in a finite product of infinite Grassmannians, such that they will be locally closed subschemes of these Grassmannians which represent a kind of flag…

Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field. Criteria are given which characterize existence of a fine or coarse moduli space classifying, up to isomorphism, the representations of $\Lambda$ with fixed…

We study moduli spaces $\mathcal{N}$ of rank 2 stable reflexive sheaves on $\mathbb{P}^3$. Fixing Chern classes $c_1$, $c_2$, and summing over $c_3$, we consider the generating function $\mathsf{Z}^{\mathrm{refl}}(q)$ of Euler…

In this manuscript we prove the Bernstein inequality and develop the theory of holonomic D-modules for rings of invariants of finite groups in characteristic zero, and for strongly F-regular finitely generated graded algebras with FFRT in…