PBW filtration and bases for symplectic lie algebras

Evgeny Feigin; Ghislain Fourier; Peter Littelmann

doi:10.1093/imrn/rnr014

PBW filtration and bases for symplectic lie algebras

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 sp_2n. This filtration is induced by the standard degree filtration on U(n^-). We give a description of the associated graded S(n^-)-module grV(λ) in terms of generators and relations. We also construct a basis of grV(λ). As an application we derive a graded combinatorial formula for the character of V(λ) and obtain a new class of bases of the modules V(λ).

Original language	English
Pages (from-to)	5760-5784
Number of pages	25
Journal	International Mathematics Research Notices
Volume	2011
Issue number	24
DOIs	https://doi.org/10.1093/imrn/rnr014
State	Published - 1 Jan 2011
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1093/imrn/rnr014

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title = "PBW filtration and bases for symplectic lie algebras",

abstract = "We study the PBW filtration on the highest weight representations V (λ) of sp2n. This filtration is induced by the standard degree filtration on U(n-). We give a description of the associated graded S(n-)-module grV(λ) in terms of generators and relations. We also construct a basis of grV(λ). As an application we derive a graded combinatorial formula for the character of V(λ) and obtain a new class of bases of the modules V(λ).",

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

note = "Funding Information: This work was partially supported by the Russian President Grant MK-281.2009.1, the RFBR Grants 09-01-00058 and NSh-3472.2008.2, by Pierre Deligne fund based on his 2004 Balzan prize in mathematics (to E.F.) and was partially supported by the DFG project “Kombinatorische Beschrei-bung von Macdonald und Kostka-Foulkes Polynomen” (to G.F.). This work was also partially supported by the priority program SPP 1388 of the German Science Foundation (to P.L.).",

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doi = "10.1093/imrn/rnr014",

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T1 - PBW filtration and bases for symplectic lie algebras

AU - Feigin, Evgeny

AU - Fourier, Ghislain

AU - Littelmann, Peter

N1 - Funding Information: This work was partially supported by the Russian President Grant MK-281.2009.1, the RFBR Grants 09-01-00058 and NSh-3472.2008.2, by Pierre Deligne fund based on his 2004 Balzan prize in mathematics (to E.F.) and was partially supported by the DFG project “Kombinatorische Beschrei-bung von Macdonald und Kostka-Foulkes Polynomen” (to G.F.). This work was also partially supported by the priority program SPP 1388 of the German Science Foundation (to P.L.).

PY - 2011/1/1

Y1 - 2011/1/1

N2 - We study the PBW filtration on the highest weight representations V (λ) of sp2n. This filtration is induced by the standard degree filtration on U(n-). We give a description of the associated graded S(n-)-module grV(λ) in terms of generators and relations. We also construct a basis of grV(λ). As an application we derive a graded combinatorial formula for the character of V(λ) and obtain a new class of bases of the modules V(λ).

AB - We study the PBW filtration on the highest weight representations V (λ) of sp2n. This filtration is induced by the standard degree filtration on U(n-). We give a description of the associated graded S(n-)-module grV(λ) in terms of generators and relations. We also construct a basis of grV(λ). As an application we derive a graded combinatorial formula for the character of V(λ) and obtain a new class of bases of the modules V(λ).

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U2 - 10.1093/imrn/rnr014

DO - 10.1093/imrn/rnr014

M3 - مقالة

SN - 1073-7928

VL - 2011

SP - 5760

EP - 5784

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 24

ER -

PBW filtration and bases for symplectic lie algebras

Abstract

All Science Journal Classification (ASJC) codes

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