Work

Imaginary elements and crystals for quantum groups

Year: 2026

Type: preprint

Abstract: In this paper, we introduce the notion of stable imaginary elements in quantum groups and use crystal basis theory to construct explicit one-parameter families of such elements for all finite types. We show that all of Leclerc's examples of imaginary elements are stable imaginary. Using the generalized quantum Schur--Weyl duality, we also construct explicit examples of corresponding imaginary modules over quantum affine algebras of untwisted affine types.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.32040

Authors: Lee, Kyu-Hwan, Park, Euiyong

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Research Foundation of Korea, Ministry of Science and ICT, South Korea

Awards: G1966264416, G3033566463, G3812690899, G4219647486, G6593274563, Collaborative Research: AIMing: Advancing Combinatorics and Number Theory with AI

OpenAlex ID: W7223702512

Cites: 5

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Related to: 10