Presentations of the principal subspaces of the higher-level standard <(sl(3))over cap>-modules

被引：20

作者：

Sadowski, Christopher ^{[1
]}

机构：

[1] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2015年 / 219卷 / 06期

关键词：

STOYANOVSKYS TYPE SUBSPACES; AFFINE LIE-ALGEBRA; COMBINATORIAL BASES; VERTEX OPERATORS; CHARACTERS; A(1)((1))-MODULES; REPRESENTATIONS; IDENTITIES;

D O I：

10.1016/j.jpaa.2014.09.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using the theory of vertex operator algebras and intertwining operators, we obtain presentations for the principal subspaces of all the standard <(sl(3))over cap>-modules. Certain of these presentations had been conjectured and used in work of Calinescu to construct exact sequences leading to the graded dimensions of certain principal subspaces. We prove the conjecture in its full generality for all standard <(sl(3))over cap>-modules. We then provide a conjecture for the case of <(sl(n + 1))over cap>. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：2300 / 2345

页数：46

共 42 条

[1]

ANDREWS GE, 1976, ENCY MATH APPL, V2

[2]

[Anonymous], ARXIVHEPTH9308079

[3]

[Anonymous], 1990, INFINITE DIMENSIONAL, DOI DOI 10.1017/CBO9780511626234

[4] Fermionic characters and arbitrary highest-weight integrable (sl)over-capr+1-modules [J].

Ardonne, E ;

Kedem, R ;

Stone, M .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2006, 264 (02) :427-464

[5] COMBINATORIAL BASES OF FEIGIN-STOYANOVSKY'S TYPE SUBSPACES OF LEVEL 2 STANDARD MODULES FOR D4(1) [J].

Baranovic, Ivana .

COMMUNICATIONS IN ALGEBRA, 2011, 39 (03) :1007-1051

[6] VERTEX ALGEBRAS, KAC-MOODY ALGEBRAS, AND THE MONSTER [J].

BORCHERDS, RE .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1986, 83 (10) :3068-3071

[7] Combinatorial bases of principal subspaces for the affine Lie algebra of type B2(1) [J].

Butorac, Marijana .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2014, 218 (03) :424-447

[8] Vertex-algebraic structure of the principal subspaces of certain A1(1)-modules, II:: Higher-level case [J].

Calinescu, C. ;

Lepowsky, J. ;

Milas, A. .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2008, 212 (08) :1928-1950

[9] Vertex-algebraic structure of the principal subspaces of certain A1(1)-modules, I:: Level one case [J].

Calinescu, C. ;

Lepowsky, J. ;

Milas, A. .

INTERNATIONAL JOURNAL OF MATHEMATICS, 2008, 19 (01) :71-92

[10] Vertex-algebraic structure of the principal subspaces of level one modules for the untwisted affine Lie algebras of types A, D, E [J].

Calinescu, C. ;

Lepowsky, J. ;

Milas, A. .

JOURNAL OF ALGEBRA, 2010, 323 (01) :167-192

← 1 2 3 4 5 →