Finite-Dimensional Representations of Hyper Multicurrent and Multiloop Algebras

被引：2

作者：

Bianchi, Angelo ^{[1
]}

Chamberlin, Samuel ^{[2
]}

机构：

[1] Univ Fed Sao Paulo UNIFESP, Dept Sci & Technol, Sao Paulo, Brazil

[2] Park Univ, Dept Math & Stat, Parkville, MO 64152 USA

来源：

ALGEBRAS AND REPRESENTATION THEORY | 2021年 / 24卷 / 02期

关键词：

Hyperalgebras; Multicurrent algebras; Multiloop algebras; Weyl modules; UNIVERSAL ENVELOPING-ALGEBRAS; LOCAL WEYL MODULES; INTEGRAL BASES; DEMAZURE;

D O I：

10.1007/s10468-020-09955-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate the categories of finite-dimensional representations of multicurrent and multiloop hyperalgebras in positive characteristic, i.e., the hyperalgebras associated to the multicurrent algebras g circle times DOUBLE-STRUCK CAPITAL C[t1, and to the multiloop algebras g circle times DOUBLE-STRUCK CAPITAL C[t1 +/- 1, horizontal ellipsis ,tn +/- 1]is any finite-dimensional complex simple Lie algebra. The main results are the construction of the universal finite-dimensional highest-weight modules and a classification of the irreducible modules in each category. In the characteristic zero setting we also provide a relationship between these modules.

引用

页码：453 / 472

页数：20

共 50 条

[1] Finite-Dimensional Representations of Hyper Multicurrent and Multiloop Algebras
Angelo Bianchi
Samuel Chamberlin
[J]. Algebras and Representation Theory, 2021, 24 : 453 - 472
[2] Finite-dimensional representations of hyper loop algebras
Jakelic, Dijana
De Moura, Adriano Adrega
[J]. PACIFIC JOURNAL OF MATHEMATICS, 2007, 233 (02) : 371 - 402
[3] On Multiplicity Problems for Finite-Dimensional Representations of Hyper Loop Algebras
Jakelic, Dijana
Moura, Adriano
[J]. ALGEBRAS, REPRESENTATIONS AND APPLICATIONS, 2009, 483 : 147 - +
[4] MODULI OF REPRESENTATIONS OF FINITE-DIMENSIONAL ALGEBRAS
KING, AD
[J]. QUARTERLY JOURNAL OF MATHEMATICS, 1994, 45 (180): : 515 - 530
[5] Representations of finite-dimensional Hopf algebras
Lorenz, M
[J]. JOURNAL OF ALGEBRA, 1997, 188 (02) : 476 - 505
[6] FINITE-DIMENSIONAL REPRESENTATIONS OF PI ALGEBRAS
AMITSUR, SA
SMALL, LW
[J]. JOURNAL OF ALGEBRA, 1990, 133 (02) : 244 - 248
[7] Finite-dimensional representations of quantum affine algebras
Akasaka, T
Kashiwara, M
[J]. PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 1997, 33 (05) : 839 - 867
[8] Decomposing moduli of representations of finite-dimensional algebras
Chindris, Calin
Kinser, Ryan
[J]. MATHEMATISCHE ANNALEN, 2018, 372 (1-2) : 555 - 580
[9] Finite-dimensional representations of rational Cherednik algebras
Berest, Y
Etingof, P
Ginzburg, V
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2003, 2003 (19) : 1053 - 1088
[10] FINITE-DIMENSIONAL REPRESENTATIONS OF W-ALGEBRAS
Losev, Ivan
[J]. DUKE MATHEMATICAL JOURNAL, 2011, 159 (01) : 99 - 143

← 1 2 3 4 5 →