A combinatorial model for q-characters of fundamental modules of type Dn

被引：0

作者：

Tong, Jun ^{[1
]}

Duan, Bing ^{[1
]}

Luo, Yanfeng ^{[1
]}

机构：

[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China

来源：

COMMUNICATIONS IN ALGEBRA | 2025年 / 53卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Combinatorial path models; fundamental modules; quantum affine algebras; q-characters; screening operators; FINITE-DIMENSIONAL REPRESENTATIONS; MINIMAL AFFINIZATIONS; CLUSTER ALGEBRAS; QUIVER VARIETIES; JACOBI-TRUDI; QUANTUM;

D O I：

10.1080/00927872.2024.2379491

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we introduce a combinatorial path model of representation of the quantum affine algebra of type D-n, inspired by Mukhin and Young's combinatorial path models of representations of the quantum affine algebras of types A(n) and B-n. In particular, we give a combinatorial formula for q-characters of fundamental modules of type D-n by assigning each path to a monomial or binomial. By counting our paths, a new expression on dimensions of fundamental modules of type D-n is obtained.

引用

页码：467 / 488

页数：22

共 15 条

[1] Path description for q-characters of fundamental modules in type C
Jang, Il-Seung
COMMUNICATIONS IN ALGEBRA, 2024, 52 (03) : 1237 - 1254
[2] Path description of type B q-characters
Mukhin, E.
Young, C. A. S.
ADVANCES IN MATHEMATICS, 2012, 231 (02) : 1119 - 1150
[3] A cluster algebra approach to q-characters of Kirillov-Reshetikhin modules
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Leclerc, B.
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2016, 18 (05) : 1113 - 1159
[4] Combinatorics of the q-characters of Hernandez-Leclerc modules
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Duan, Bing
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JOURNAL OF ALGEBRA, 2022, 605 : 253 - 295
[5] Dorey's Rule and the q-Characters of Simply-Laced Quantum Affine Algebras
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[6] Cluster realization of Weyl groups and q-characters of quantum affine algebras
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[7] Invariants of Weyl Group Action and q-characters of Quantum Affine Algebras
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Algebras and Representation Theory, 2023, 26 : 3167 - 3183
[8] Cluster realization of Weyl groups and q-characters of quantum affine algebras
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LETTERS IN MATHEMATICAL PHYSICS, 2021, 111 (01)
[9] Invariants of Weyl Group Action and q-characters of Quantum Affine Algebras
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ALGEBRAS AND REPRESENTATION THEORY, 2023, 26 (06) : 3167 - 3183
[10] t-Analogs of q-Characters of Quantum Affine Algebras of Type E6, E7, E8
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REPRESENTATION THEORY OF ALGEBRAIC GROUPS AND QUANTUM GROUPS, 2010, 284 : 257 - 272

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