An Algebra Associated with a Flag in a Subspace Lattice over a Finite Field and the Quantum Affine Algebra

  • Yuta Watanabe Tohoku university
Keywords: Subspace lattice, Young diagram, Incidence algebra, Quantum affine algebra

Abstract

In this paper, we introduce an algebra $\mathcal{H}$ from a subspace lattice with respect to a fixed flag which contains its incidence algebra as a proper subalgebra. We then establish a relation between the algebra $\mathcal{H}$ and the quantum affine algebra $U_{q^{1/2}}(\widehat{\mathfrak{sl}}_2)$, where $q$ denotes the cardinality of the base field. It is an extension of the well-known relation between the incidence algebra of a subspace lattice and the quantum algebra $U_{q^{1/2}}(\mathfrak{sl}_2)$. We show that there exists an algebra homomorphism from $U_{q^{1/2}}(\widehat{\mathfrak{sl}}_2)$ to $\mathcal{H}$ and that any irreducible module for $\mathcal{H}$ is irreducible as an $U_{q^{1/2}}(\widehat{\mathfrak{sl}}_2)$-module.

Author Biography

Yuta Watanabe, Tohoku university

Current affiliation: National Institute of Technology, Ube College

Email: ywatanabe@ube-k.ac.jp

Published
2018-11-02
Article Number
P4.31