PBW filtration and bases for irreducible modules in type An

Evgeny Feigin; Ghislain Fourier; Peter Littelmann

doi:10.1007/s00031-010-9115-4

PBW filtration and bases for irreducible modules in type A_n

Evgeny Feigin
, Ghislain Fourier
, Peter Littelmann

Research output: Contribution to journal › Article › peer-review

Abstract

We study the PBW filtration on the highest weight representations V(λ) 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(λ) in terms of generators and relations. We also construct a basis of gr V(λ). As an application we derive a graded combinatorial character formula for V(λ), and we obtain a new class of bases of the modules V(λ) conjectured by Vinberg in 2005.

Original language	English GB
Pages (from-to)	71-89
Number of pages	19
Journal	Transformation Groups
Volume	16
Issue number	1
DOIs	https://doi.org/10.1007/s00031-010-9115-4
State	Published - Mar 2011
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

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10.1007/s00031-010-9115-4

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title = "PBW filtration and bases for irreducible modules in type An",

abstract = "We study the PBW filtration on the highest weight representations V(λ) of SLn+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(λ) in terms of generators and relations. We also construct a basis of gr V(λ). As an application we derive a graded combinatorial character formula for V(λ), and we obtain a new class of bases of the modules V(λ) conjectured by Vinberg in 2005.",

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AU - Fourier, Ghislain

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N2 - We study the PBW filtration on the highest weight representations V(λ) of SLn+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(λ) in terms of generators and relations. We also construct a basis of gr V(λ). As an application we derive a graded combinatorial character formula for V(λ), and we obtain a new class of bases of the modules V(λ) conjectured by Vinberg in 2005.

AB - We study the PBW filtration on the highest weight representations V(λ) of SLn+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(λ) in terms of generators and relations. We also construct a basis of gr V(λ). As an application we derive a graded combinatorial character formula for V(λ), and we obtain a new class of bases of the modules V(λ) conjectured by Vinberg in 2005.

UR - https://www.scopus.com/pages/publications/79953123711

U2 - 10.1007/s00031-010-9115-4

DO - 10.1007/s00031-010-9115-4

M3 - مقالة

SN - 1083-4362

VL - 16

SP - 71

EP - 89

JO - Transformation Groups

JF - Transformation Groups

IS - 1

ER -

PBW filtration and bases for irreducible modules in type A_n

Abstract

ASJC Scopus subject areas

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