Related papers: p-DG cyclotomic nilHecke algebras

We categorify tensor products of the fundamental representation of quantum $\mathfrak{sl}_2$ at prime roots of unity building upon earlier work where a tensor product of two Weyl modules was categorified.

The purpose of this paper is to study categorifications of tensor products of finite dimensional modules for the quantum group for sl(2). The main categorification is obtained using certain Harish-Chandra bimodules for the complex Lie…

We give a complete picture of when the tensor product of an induced module and a Weyl module is a tilting module for the algebraic group $SL_2$ over an algebraically closed field of characteristic $p$. Whilst the result is recursive by…

We define a derivation on the enhanced nilHecke algebra yielding a p-dg algebra when working over a field of characteristic p. We define functors on the category of p-dg modules resulting in an action of small quantum sl2 on the…

We equip the odd nilHecke algebra and its associated thick calculus category with digrammatically local differentials. The resulting differential graded Grothendieck groups are isomorphic to two different forms of the positive part of…

We categorify the Beilinson-Lusztig-MacPherson integral form of quantum sl(2) specialized at a prime root of unity.

This is the first part of a series of two papers aiming to construct a categorification of the braiding on tensor products of Verma modules, and in particular of the Lawrence--Krammer--Bigelow representations. \\ In this part, we categorify…

We establish several results concerning tensor products, q-characters, and the block decomposition of the category of finite-dimensional representations of quantum affine algebras in the root of unity setting. In the generic case, a Weyl…

We classify semisimple module categories over the tensor category of representations of quantum SL(2) extending previous results to the roots of unity and positive characteristic cases.

We construct a dg-enhancement of KLRW algebras that categorifies the tensor product of a universal $\mathfrak{sl}_2$ Verma module and several integrable irreducible modules. When the integrable modules are two-dimensional, we construct a…

We categorify one half of the small quantum sl(2) at a prime root of unity. An extension of this construction to an arbitrary simply-laced case is proposed.

We study the bimodule structure of the quantum function algebra at roots of 1 and prove that it admits an increasing filtration with factors isomorphic to the tensor products of the dual of Weyl modules $V_\lambda^* \otimes V_{- \omega_0…

We show that in ADE type the trace of Webster's categorification of a tensor product of irreducibles for the quantum group is isomorphic to a tensor product of Weyl modules for the current algebra $\dot{U}(\mathfrak{g}[t])$. This extends a…

We give a purely geometric categorification of tensor products of finite-dimensional simple $U_q(sl_2)$-modules and $R$-matrices on them. The work is developed in the framework of category of perverse sheaves and the categorification…

We relate the classes of unitary and calibrated representations of cyclotomic Hecke algebras and, in particular, we show that for the most important deformation parameters these two classes coincide. We classify these representations in…

We give a classification of the simple modules for the cyclotomic Hecke algebras over $\mathbb{C}$ in the modular case. We use the unitriangular shape of the decomposition matrices of Ariki-Koike algebras and Clifford theory.

In this article the simple modules over the rank-two quantized Weyl algebras at roots of unity over an algebraically closed field are classified.

We categorify an idempotented form of quantum sl2 and some of its simple representations at a prime root of unity.

Using diagrammatic methods, we define a quiver algebra depending on a prime p and show that it is the algebra underlying the category of tilting modules for SL(2) in characteristic p. Along the way we obtain a presentation for morphisms…

Recall that an algebraic module is a KG-module that satisfies a polynomial with integer coefficients, with addition and multiplication given by direct sum and tensor product. In this article we prove that if L is a component of the (stable)…