PBW filtration and bases for irreducible modules in type An

被引：72

作者：

Feigin, Evgeny ^{[1
,2
]}

Fourier, Ghislain ^{[3
]}

Littelmann, Peter ^{[3
]}

机构：

[1] Univ Higher Sch Econ, Dept Math, Moscow 101000, Russia

[2] Lebedev Phys Inst, Moscow, Russia

[3] Univ Cologne, Math Inst, D-50931 Cologne, Germany

来源：

TRANSFORMATION GROUPS | 2011年 / 16卷 / 01期

关键词：

Positive Root; Simple Root; Total Order; Vertex Operator Algebra; High Weight Vector;

D O I：

10.1007/s00031-010-9115-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the PBW filtration on the highest weight representations V(lambda) of sl(n+1). This filtration is induced by the standard degree filtration on U(n(-)). We give a description of the associated graded S(n(-))-module gr V(lambda) in terms of generators and relations. We also construct a basis of gr V(lambda). As an application we derive a graded combinatorial character formula for V(lambda), and we obtain a new class of bases of the modules V(lambda) conjectured by Vinberg in 2005.

引用

页码：71 / 89

页数：19

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