Details

Autor(en) / Beteiligte

• Inoue, Rei
• Yamazaki, Takao

Titel

Invariants of Weyl Group Action and q-characters of Quantum Affine Algebras

Ist Teil von

• Algebras and representation theory, 2023-12, Vol.26 (6), p.3167-3183

Ort / Verlag

Dordrecht: Springer Netherlands

Erscheinungsjahr

2023

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Let W be the Weyl group corresponding to a finite dimensional simple Lie algebra g of rank ℓ and let m > 1 be an integer. In Inoue (Lett. Math. Phys. 111(1):32, 2021), by applying cluster mutations, a W -action on Y m was constructed. Here Y m is the rational function field on c m ℓ commuting variables, where c ∈ { 1 , 2 , 3 } depends on g . This was motivated by the q -character map χ q of the category of finite dimensional representations of quantum affine algebra U q ( g ^ ) . We showed in Inoue (Lett. Math. Phys. 111(1):32, 2021) 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 i th simple root, we describe the r i -invariant subfield Y m r i of Y m .