REPRESENTATIONS OF QUANTUM AFFINE ALGEBRAS OF TYPE BN

被引：6

作者：

Brito, Matheus ^{[1
]}

Mukhin, Evgeny ^{[2
]}

机构：

[1] Univ Estadual Campinas, Dept Matemat, BR-13083859 Campinas, SP, Brazil

[2] Indiana Univ Purdue Univ, 402 N Blackford St,LD 270, Indianapolis, IN 46202 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2017年 / 369卷 / 04期

基金：

巴西圣保罗研究基金会;

关键词：

FINITE-DIMENSIONAL REPRESENTATIONS; MINIMAL AFFINIZATIONS; TENSOR-PRODUCTS; JACOBI-TRUDI; Q-CHARACTERS; COMBINATORICS; TABLEAUX; MODULES; LIMITS; PATHS;

D O I：

10.1090/tran/6735

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study finite-dimensional representations of quantum affine algebras of type B-N. We show that a module is tame if and only if it is thin. In other words, the Cartan currents are diagonalizable if and only if all joint generalized eigenspaces have dimension one. We classify all such modules and describe their q-characters. In some cases, the q-characters are described by super standard Young tableaux of type (2N vertical bar 1).

引用

页码：2775 / 2806

页数：32

共 27 条

[1] BRAID GROUP ACTION AND QUANTUM AFFINE ALGEBRAS [J].

BECK, J .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1994, 165 (03) :555-568

[2] An algebraic characterization of the affine canonical basis [J].

Beck, J ;

Chari, V ;

Pressley, A .

DUKE MATHEMATICAL JOURNAL, 1999, 99 (03) :455-487

[3] HOOK-YOUNG DIAGRAMS, COMBINATORICS AND REPRESENTATIONS OF LIE-SUPERALGEBRAS [J].

BERELE, A ;

REGEV, A .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 8 (02) :337-339

[4] Minimal affinizations of representations of quantum groups: The irregular case [J].

Chari, V ;

Pressley, A .

LETTERS IN MATHEMATICAL PHYSICS, 1996, 36 (03) :247-266

[5] MINIMAL AFFINIZATIONS OF REPRESENTATIONS OF QUANTUM GROUPS - THE NONSIMPLY-LACED CASE [J].

CHARI, V ;

PRESSLEY, A .

LETTERS IN MATHEMATICAL PHYSICS, 1995, 35 (02) :99-114

[6] Minimal affinizations of representations of quantum groups: The rank 2 case [J].

Chari, V .

PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 1995, 31 (05) :873-911

[7] Minimal affinizations of representations of quantum groups: The simply laced case [J].

Chari, V ;

Pressley, A .

JOURNAL OF ALGEBRA, 1996, 184 (01) :1-30

[8]

Chari V., 1995, CMS C P, V16, P59

[9]

Chari V., 1994, A guide to quantum groups

[10] The R-matrix for non-twisted affine quantum algebras [J].

Damiani, I .

ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 1998, 31 (04) :493-523

← 1 2 3 →