Two maps on affine type A crystals and Hecke algebras

TL;DR

This paper explores two maps on partitions within the context of affine type A crystal bases and Hecke algebra representations, revealing their interconnected roles in quantum group theory and algebraic structures.

Contribution

It introduces and describes two specific maps on partitions that arise naturally in the crystal basis theory and Hecke algebra representations, linking these areas.

Findings

Description of two maps on partitions in affine type A crystals

Connection between crystal isomorphisms and Hecke algebra representations

Insight into the structure of multipartitions in quantum groups

Abstract

We use the crystal isomorphisms of the Fock space to describe two maps on partitions and multipartitions which naturally appear in the crystal basis theory for quantum groups in affine type A and in the representation theory of Hecke algebras of type G(l, l, n).