Based modules over the $ı$quantum group of type AI

Abstract

This paper studies classical weight modules over the $ı$quantum group ${\mathbf{U}}^{ı}$ of type AI. We introduce the notion of based ${\mathbf{U}}^{ı}$-modules by generalizing the notion of based modules over the quantum groups. We prove that each finite-dimensional irreducible classical weight ${\mathbf{U}}^{ı}$-module with integer highest weight is a based ${\mathbf{U}}^{ı}$-module. As a byproduct, a new combinatorial formula for the branching rule from ${\mathfrak{sl}}_n$ to ${\mathfrak{so}}_n$ is obtained.

arXiv comment68 pages

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Cited by in corpus (2)

• Crystal bases of modified $ı$quantum groups of certain quasi-split types
• A new tableau model for irreducible polynomial representations of the orthogonal group