Unipotent quantum coordinate ring and cominuscule prefundamental representations

Il Seung Jang; Jae Hoon Kwon; Euiyong Park

doi:10.1016/j.jalgebra.2025.01.031

Unipotent quantum coordinate ring and cominuscule prefundamental representations

Il Seung Jang
, Jae Hoon Kwon
, Euiyong Park

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We continue the study of realization of the prefundamental modules L_r,a^±, introduced by Hernandez and Jimbo, in terms of unipotent quantum coordinate rings as in [23]. We show that the ordinary character of L_r,a^± is equal to that of the unipotent quantum coordinate ring U_q⁻(w_r) associated to fundamental r-th coweight. When r is cominuscule, we prove that there exists a U_q(b)-module structure on U_q⁻(w_r), which is isomorphic to L_{r,aη_r}^± for some η_r∈C^×.

Original language	English
Pages (from-to)	260-303
Number of pages	44
Journal	Journal of Algebra
Volume	673
DOIs	https://doi.org/10.1016/j.jalgebra.2025.01.031
State	Published - 1 Jul 2025

Keywords

Braid group symmetries
Prefundamental modules
Quantum affine algebras
Unipotent quantum coordinate rings

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10.1016/j.jalgebra.2025.01.031

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title = "Unipotent quantum coordinate ring and cominuscule prefundamental representations",

abstract = "We continue the study of realization of the prefundamental modules Lr,a±, introduced by Hernandez and Jimbo, in terms of unipotent quantum coordinate rings as in [23]. We show that the ordinary character of Lr,a± is equal to that of the unipotent quantum coordinate ring Uq−(wr) associated to fundamental r-th coweight. When r is cominuscule, we prove that there exists a Uq(b)-module structure on Uq−(wr), which is isomorphic to Lr,aηr± for some ηr∈C×.",

keywords = "Braid group symmetries, Prefundamental modules, Quantum affine algebras, Unipotent quantum coordinate rings",

author = "Jang, \{Il Seung\} and Kwon, \{Jae Hoon\} and Euiyong Park",

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doi = "10.1016/j.jalgebra.2025.01.031",

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T1 - Unipotent quantum coordinate ring and cominuscule prefundamental representations

AU - Jang, Il Seung

AU - Kwon, Jae Hoon

AU - Park, Euiyong

PY - 2025/7/1

Y1 - 2025/7/1

N2 - We continue the study of realization of the prefundamental modules Lr,a±, introduced by Hernandez and Jimbo, in terms of unipotent quantum coordinate rings as in [23]. We show that the ordinary character of Lr,a± is equal to that of the unipotent quantum coordinate ring Uq−(wr) associated to fundamental r-th coweight. When r is cominuscule, we prove that there exists a Uq(b)-module structure on Uq−(wr), which is isomorphic to Lr,aηr± for some ηr∈C×.

AB - We continue the study of realization of the prefundamental modules Lr,a±, introduced by Hernandez and Jimbo, in terms of unipotent quantum coordinate rings as in [23]. We show that the ordinary character of Lr,a± is equal to that of the unipotent quantum coordinate ring Uq−(wr) associated to fundamental r-th coweight. When r is cominuscule, we prove that there exists a Uq(b)-module structure on Uq−(wr), which is isomorphic to Lr,aηr± for some ηr∈C×.

KW - Braid group symmetries

KW - Prefundamental modules

KW - Quantum affine algebras

KW - Unipotent quantum coordinate rings

UR - https://www.scopus.com/pages/publications/86000716768

U2 - 10.1016/j.jalgebra.2025.01.031

DO - 10.1016/j.jalgebra.2025.01.031

M3 - Article

AN - SCOPUS:86000716768

SN - 0021-8693

VL - 673

SP - 260

EP - 303

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Unipotent quantum coordinate ring and cominuscule prefundamental representations

Abstract

Keywords

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