Related papers: On the minimal parabolic induction

We generalize our work on Carlitz prime power torsion extension to torsion extensions of Drinfeld modules of arbitrary rank. As in the Carlitz case, we give a description of these extensions in terms of evaluations of Anderson generating…

The goal of the present paper is to obtain new free field realizations of affine Kac-Moody algebras motivated by geometric representation theory for generalized flag manifolds of finite-dimensional semisimple Lie groups. We provide an…

We study primitive ideals in the enveloping algebra of finitary locally finite infinite-dimensional complex Lie algebras. In particular we investigate the annihilators of the simple objects in the category of tensor modules. This category…

We introduce the notion of a strong minuscule element, and prove that the dominant integral weight associated to a strong minuscule element is the fundamental weight corresponding to a short simple root. In addition, we enumerate the strong…

In this paper we shall prove that the subalgebra generated over the integers by the divided powers of the Drinfeld generators $x_r^{\pm}$ of the Kac-Moody algebra of type $A_2^{(2)}$ is an integral form (strictly smaller than Mitzman's (see…

We consider how a vertex operator algebra can be extended to an abelian intertwining algebra by a family of weak twisted modules which are {\em simple currents} associated with semisimple weight one primary vectors. In the case that the…

We develop $L$-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of cubic Hecke $L$-functions of prime moduli over the Eisenstein field using multiple Dirichlet series under the…

In this paper, we prove the Eichler cohomology theorem of weakly parabolic generalized modular forms of real weights on subgroups of finite index in the full modular group. We explicitly establish the isomorphism for large weights by…

The theta-block conjecture proposed by Gritsenko--Poor--Yuen in 2013 characterizes Siegel paramodular forms which are simultaneously Borcherds products and additive Jacobi lifts. In this paper, we prove this conjecture for two new infinite…

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…

We construct the polynomial induction functor, which is the right adjoint to the restriction functor from the category of polynomial representations of a general linear group to the category of representations of its Weyl group. This…

Zagier introduced special bases for weakly holomorphic modular forms to give the new proof of Borcherds' theorem on the infinite product expansions of integer weight modular forms on $\SL_2(\ZZ)$ with a Heegner divisor. These good bases…

We define the notion of index-module for a couple of A-lattices in a vector space, A being a Dedekind ring. We apply this notion to prove by elementary means that a weak Gras conjecture (i.e for irreducible nontrivial Q-characters) holds…

We prove a variant of Emerton's conjecture concerning the right derived functors of the ordinary parts functor $\operatorname{Ord}_P^G$. This functor plays an important role in the theory of mod $p$ representations of $p$-adic reductive…

Let $L$ be a finite-dimensional Lie algebra over a field of non-zero characteristic and let $S$ be a subalgebra. Suppose that $X$ is a finite set of finite-dimensional $L$-modules. Let $D$ be the category of all finite-dimensional…

In this paper we study certain fundamental and distinguished subsets of weights of an arbitrary highest weight module over a complex semisimple Lie algebra. These sets ${\rm wt}_J \mathbb{V}^\lambda$ are defined for each highest weight…

We decompose the K-theory space of a Waldhausen category in terms of its Dwyer-Kan simplicial localization. This leads to a criterion for functors to induce equivalences of K-theory spectra that generalizes and explains many of the criteria…

We prove that the parabolic induction functor on BGG-category $\mathcal{O}$ associated to a complex reductive Lie algebra is gradable, that is, lifts to graded category $\mathcal{O}$ as constructed by Beilinson-Ginzburg-Soergel. Graded…

We construct a large class of morphisms, which we call partial morphisms, of groupoids that induce $*$-morphisms of maximal and minimal groupoid $C^*$-algebras. We show that the association of a groupoid to its maximal (minimal) groupoid…

We study the restricted Verma modules of an affine Kac-Moody algebra at the critical level with special emphasis on their Jordan-H"older multiplicities. The Feigin-Frenkel conjecture gives a formula for these multiplicities that involves…