Related papers: On character formulas for simple and tilting modul…

Let G be a semisimple group over an algebraically closed field of characteristic p>0. We give a (partly conjectural) simple, closed formula for the character of many indecomposable tilting rational G-modules, assuming that p is large.

We describe an algorithm, which - given the characters of tilting modules and assuming that Donkin's tilting conjecture is true - computes the characters of simple modules for an algebraic group in any characteristic.

We establish a character formula for indecomposable tilting modules for connected reductive groups in characteristic p in terms of p-Kazhdan-Lusztig polynomials, for p>h the Coxeter number. Using results of Andersen, one may deduce a…

These notes are our contribution to the Proceedings of the ICM 2026. We discuss some results we have obtained (in part jointly with coauthors) regarding the representation theory of reductive algebraic groups over algebraically closed…

In this paper we prove a character formula expressing the classes of simple representations in the principal block of a simply-connected semisimple algebraic group G in terms of baby Verma modules, under the assumption that the…

Let $\mathcal O_p$ denote the characteristic $p>0$ version of the ordinary category $\mathcal O$ for a semisimple complex Lie algebra. In this paper we give some (formal) character formulas in $\mathcal O_p$. First we concentrate on the…

Let G be a semisimple, simply-connected algebraic group over an algebraically closed field of characteristic p > 0. We observe that the tensor product of the Steinberg module with a minuscule module is always indecomposable tilting.…

We give a cohomological treatment of a character theory for (g,K)-modules. This leads to a nice formalism extending to large categories of not necessarily admissible (g,K)-modules. Due to results of Hecht, Schmid and Vogan the classical…

In this paper the authors provide a complete answer to Donkin's Tilting Module Conjecture for all rank $2$ semisimple algebraic groups and $\text{SL}_{4}(k)$ where $k$ is an algebraically closed field of characteristic $p>0$. In the…

These notes present an application of the geometric Satake equivalence to the description of characters of indecomposable tilting modules for reductive algebraic groups over fields of positive characteristic, obtained in joint work with G.…

For an arbitrary infinite field k of characteristic p > 0, we describe the structure of a block of the algebraic monoid M_n(k) (all n x n matrices over k), or, equivalently, a block of the Schur algebra S(n,p), whose simple modules are…

In this paper we propose a new approach to tilting modules for reductive algebraic groups in positive characteristic. We conjecture that translation functors give an action of the (diagrammatic) Hecke category of the affine Weyl group on…

We derive a parameterization of simple modules for the cyclotomic Hecke algebras of type $G(r,p,n)$ over field of any (coprime to $p$) characteristic. We give explicit formulas for the number of simple modules over these cyclotomic Hecke…

We establish a canonical basis character formula for the irreducible modules in arbitrary parabolic BGG-type categories, including the category of finite-dimensional modules, for finite $W$-superalgebras of type $A$. These categories…

We derive decomposition formulas for supercharacters of quantum affine ortho-symplectic superalgebras and twisted quantum affine superalgebras into supercharacters of their finite-type quantum sub-superalgebras, by employing Cauchy-type…

Let G be an almost simple, simply connected algebraic group over an algebraically closed field of characteristic p>0. In this paper we restate our conjecture from 1979 on the characters of irreducible modular representations of G so that it…

Let $G$ be a simple and simply connected algebraic group over an algebraically closed field $\Bbbk$ of characteristic $p>0$. We establish an isomorphism of $G$-modules between a direct sum of modules $\text{St} \otimes \text{St}$ and a…

Let $G$ be a simple, simply connected algebraic group over an algebraically closed field of prime characteristic $p>0$. Recent work of Kildetoft and Nakano and of Sobaje has shown close connections between two long-standing conjectures of…

In this paper we construct an action of the affine Hecke category (in its "Soergel bimodules" incarnation) on the principal block of representations of a simply-connected semisimple algebraic group over an algebraically closed field of…

We study the decomposition of tensor products between a Steinberg module and a costandard module, both as a module for the algebraic group $G$ and when restricted to either a Frobenius kernel $G_r$ or a finite Chevalley group…