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

^*Corresponding author for this work

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

77 Scopus citations

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
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

Access to Document

10.1007/s00031-010-9115-4

Cite this

@article{57f2d99e3136432a88acf180b90b0e31,

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.",

author = "Evgeny Feigin and Ghislain Fourier and Peter Littelmann",

year = "2011",

month = mar,

doi = "10.1007/s00031-010-9115-4",

language = "אנגלית",

volume = "16",

pages = "71--89",

journal = "Transformation Groups",

issn = "1083-4362",

publisher = "Birkhauser Boston",

number = "1",

}

TY - JOUR

T1 - PBW filtration and bases for irreducible modules in type An

AU - Feigin, Evgeny

AU - Fourier, Ghislain

AU - Littelmann, Peter

PY - 2011/3

Y1 - 2011/3

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 - http://www.scopus.com/inward/record.url?scp=79953123711&partnerID=8YFLogxK

U2 - 10.1007/s00031-010-9115-4

DO - 10.1007/s00031-010-9115-4

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:79953123711

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

Access to Document

Other files and links

Fingerprint

Cite this