Invariants of Weyl group action and q-characters of quantum affine algebras

2022/07/20 by Rei Inoue, Takao Yamazaki, Inoue, Rei +1
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Coding theory and cryptography #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2207.09867

openalex publication_date 2022/07/20 · openalex created_date 2022/07/22 · openalex updated_date 2026/07/28

Abstract

Let W be the Weyl group corresponding to a finite dimensional simple Lie algebra \mathfrakg of rank ℓ and let m>1 be an integer. In [I21], by applying cluster mutations, a W-action on Y_m was constructed. Here Y_m is the rational function field on cmℓ commuting variables, where c ∈ \ 1, 2, 3 \ depends on \mathfrakg. This was motivated by the q-character map χ_q of the category of finite dimensional representations of quantum affine algebra U_q(\mathfrakg). We showed in [I21] that when q is a root of unity, Im χ_q is a subring of the W-invariant subfield Y_m^W of Y_m. In this paper, we give more detailed study on Y_m^W; for each reflection r_i ∈ W associated to the ith simple root, we describe the r_i-invariant subfield Y_m^r_i of Y_m.

Related

• Weyl group symmetry of q-characters
• Invariant theory for quantum Weyl algebras under finite group action
• Extremal monomials of q-characters
• The q-characters of representations of quantum affine algebras and deformations of W-algebras
• Weyl group twists and representations of quantum affine Borel algebras