Publications (9)
Canonical Basis and Macdonald Polynomials
Jonathan Beck, Igor Frenkel, Naihuan Jing
In the basic representation of realized via the algebra of symmetric functions we compare the canonical basis with the basis of Macdonald polynomials with $q=t^2…
Crystal bases and two-sided cells of quantum affine algebras
Jonathan Beck, Hiraku Nakajima
Let $\g$ be an affine Kac-Moody Lie algebra. Let $\U^+$ be the positive part of the Drinfeld-Jimbo quantum enveloping algebra associated to $\g$. We construct a basis of $\U^+$ whi…
Measuring and Eliminating Refusals in Military Large Language Models
Jack FitzGerald, Dylan Bates, Aristotelis Lazaridis +17
Military Large Language Models (LLMs) must provide accurate information to the warfighter in time-critical and dangerous situations. However, today's LLMs are imbued with safety be…
Crystal structure of level zero extremal weight modules
Jonathan Beck
We consider the crystal structure of the level zero extremal weight modules using the crystal base of the quantum affine algebra constructed by Beck, Chari and Pressley. Th…
An Algebraic Characterization of the Affine Canonical Basis
Jonathan Beck, Vyjayanthi Chari, Andrew Pressley
The canonical basis for quantized universal enveloping algebras associated to the finite--dimensional simple Lie algebras, was introduced by Lusztig. The principal technique is the…
EdgeRunner 20B: Military Task Parity with GPT-5 while Running on the Edge
Jack FitzGerald, Aristotelis Lazaridis, Dylan Bates +17
We present EdgeRunner 20B, a fine-tuned version of gpt-oss-20b optimized for military tasks. EdgeRunner 20B was trained on 1.6M high-quality records curated from military documenta…
Convex Bases of PBW type for Quantum Affine Algebras
Jonathan Beck
This note has two purposes. First we establish that the map defined in [L, (a)] is an isomorphism for certain admissible sequences. Second we show the map gives rise to…
Braid Group Action and Quantum Affine Algebras
Jonathan Beck
We lift the lattice of translations in the extended affine Weyl group to a braid group action on the quantum affine algebra. This action fixes the Heisenberg subalgebra pointwise.…
Finite dimensional representations of quantum affine algebras at roots of unity
Jonathan Beck, Victor G. Kac
We describe explicitly the canonical map Spec $\ue(\a{g})\ \rightarrow \ $Spec $\ze$, where $\ue(\a{g})$ is a quantum loop algebra at an odd root of unity $\ve$. Here $\ze$ i…